The four names of an angle are acute angle, right angle, obtuse angle, and reflex angle.
An acute angle measures less than 90 degrees.
A right angle measures exactly 90 degrees.
An obtuse angle measures greater than 90 degrees but less than 180 degrees.
A reflex angle measures greater than 180 degrees but less than 360 degrees.
It's worth noting that these names are based on the measure of the angle, an acute angle is less than 90 degrees, a right angle is exactly 90 degrees, an obtuse angle is greater than 90 degrees but less than 180 degrees, and a reflex angle is greater than 180 degrees but less than 360 degrees.
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identify the initial amount a and the growth factor b in the exponential function: f(X) = 610 • 7.54
The initial amount is 610 and the growth factor is 7.54.
What is an exponential function?
An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.
In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.
Hence, the initial amount is 610 and the growth factor is 7.54.
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The initial amount is 610 and the growth factor is 7.54.
What is an exponential function?An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.
What is growth factor?A growth factor is a naturally occurring substance that stimulates a cell to grow, divide, and differentiate. Growth factors are typically proteins or peptides that bind to specific receptors on the surface of cells, triggering signaling pathways that lead to cell proliferation and survival.
In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.
Hence, the initial amount is 610 and the growth factor is 7.54.
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For m(x)=
-3/4x+6, find the value of x for which m(x) = 0.
The value of x when m(x) = 0 is 8.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.
The given function is,
m(x) = -3/4 x + 6
Here the value of m(x) depends on the value of x.
m(x) = 0
-3/4 x + 6 = 0
-3/4 x = -6
x = -6 ÷ -3/4
x = 6 × 4/3
x = 8
Hence when m(x) = 0, the value of x is 8.
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Answer to this question pls
It would change to about 9. 960 atmospheres
How to determine the valueFollowing the Boyle's law of gases which states that the product of pressure and volume is exactly a constant for an ideal gas.
This is represented as;
PV = K
then,
P₁V₁ = P₂V₂
From the information given, we have that;
P₁ = 8.9 atmospheresP₂ = unknownV₁ = 4. 7 litersV₂ = 4. 2 litersNow, substitute the values
8. 9(4. 7) = P₂(4. 2)
mulitply the values
41. 83 = P₂(4. 2)
Divide both sides by 4.2
P₂ = 9. 960 atmospheres
Hence, the value is 9. 960 atmospheres
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At an archeological site, the remains of two ancient step pyramids are congruent . If ABCD cong EFGH find each of the following . (Diagrams are to scale. )
The measurements are found using congruency.
What does congruency mean?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
It is given that ABCD ≅ EFGH :
According to congruency,
22. AD = EH, so AD = 335 ft.
23. GH= CD, so GH = 45ft.
24. m∠GHE = m∠CDA, so m∠GHE= 52°
25. m∠BAD= m∠FEH, so m∠BAD= 52°
26. EF= AB, so EF= 45ft
27. BC= FG, so BC= 280ft
28. m∠DCB= m∠HGF, so m∠DCB= 128°
29. m∠EFG= m∠ABC, so m∠EFG= 128°
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What are the 3 segments?
Business-to-Business (B2B): This segment involves transactions between two businesses, Business-to-Consumer (B2C): This segment involves transactions between a business and a consumer and Consumer-to-Consumer (C2C): This segment involves transactions between two consumers.
1. Business-to-Business (B2B): This segment involves transactions between two businesses. Examples of B2B include sales of raw materials by a manufacturer to a wholesaler or the sale of supplies by an office supply company to a retailer.
2. Business-to-Consumer (B2C): This segment involves transactions between a business and a consumer. Examples of B2C include online retailers selling products directly to consumers, subscription services, and digital content providers.
3. Consumer-to-Consumer (C2C): This segment involves transactions between two consumers. Examples of C2C include online marketplaces, auctions, and classifieds where individuals can buy and sell items to other individuals.
the complete question is : What are the 3 segments of e-commerce ?
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6) The area of a triangle is A = bh-2. If the base (b) is H untis and the
height (h) Is 7 units, what is the area of the triangle?
I
Answer:
The area of a triangle can be calculated using the formula A = 1/2 * b * h, where b is the base and h is the height of the triangle. In this case, if the base of the triangle is H units and the height is 7 units, the area of the triangle would be A = 1/2 * H * 7 = 3.5 * H.
Step-by-step explanation:
Is 2 a positive number?
Answer:
the 2 positive of number is
Step-by-step explanation:
2_:3+23*3⅔+09=2465
You need to put equation signs in between the 6. 1 gross = 144
The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Place the arithmetic symbol between the 6 times 6 to become one. Then we have
⇒ 6 + 6 - 6 - 6 + 6 / 6
⇒ 1
The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.
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f(x) and g(x) below, find the value of (fog)(-8).
f(x) = 3x²-3x - 8
g(x) = -x - 7
Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.
Function: A DefinitionA function is a relationship between a collection of sources or one product for each input. Simply described, a function is a group of equations linked to a single, distinct output. A declaration, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). When a rules of this kind is employed, there is just one output. by photographer Alex Federspiel. This sentence provides a y=x2 example. Any input for x has only one output for y. Since x is indeed the input value, y is, by definition, a function of x.
Here,
Given :
f(x) = 3x²-3x - 8
g(x) = -x - 7
To find : fog)(-8)= ?
Thus,
We find
=> F(g(x)) => 3g(x)² -3g(x) - 8
=> f(-x-7) =3⋅(-x-7)²-3⋅(-x-7)-8
At x =-8
=> 3(-8-7)² - 3(-8-7)-8
=> 3(225)-3(15) -8
=> 675 - 45 -8
=> 622
Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.
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Geometry - Should be pretty easy
Answer:
DQR
Step-by-step explanation:
DEF is complentary to DQR
Answer:
∆DQR
Step-by-step explanation:
You want the similarity statement if the triangles shown are similar.
SimilarityTriangles will be similar if they have congruent corresponding angles, or proportional corresponding sides.
No angles are shown in the figure, but side lengths are given.
We expect that if the triangles are similar that the corresponding sides will be ...
DE ⇔ DQEF ⇔ QRFD ⇔ RDProportionThe attached calculator display shows the ratios of these side lengths are the same: 14/3. That means ...
∆DEF ~ ∆DQR
<95141404393>
2x-(x+5)=-1
Solve for x.
Answer:
x=4
Step-by-step explanation:
2x-(x+5)=-1
Solve for x
Distribute the minus sign
2x-x-5=-1
Combine like terms
x -5 = -1
Add 5 to each side
x-5+5 = -1+5
x=4
[tex]2x-(x+5)=-1[/tex]
Distribute negative sign:
[tex]2x+-1(x+5)=-1[/tex]
[tex]2x+-x+-5=-1[/tex]
Combine Like Terms:
[tex](2x+-x)+(-5)=-11[/tex]
[tex]x-5=-1[/tex]
Add 5 to both sides:
[tex]x-5+5=-1+5[/tex]
[tex]\fbox{x = 4}[/tex]
Meada scored 24 points. If this was 4 less than the number
of points scored Jill scored, how many points did Jill score?
Define a variable. Then write an equation that could be
used to solve the problem.
Answer:
the answer is 28
Step-by-step explanation:
Maeda scored 24 points and if 4 less then jill
x is variable
x-4=24 add 4 on both sides
x=28
Hi! I need Help With The Bottom Answers Someone Already Answered The Top So Just The Bottom Questions!
F:4+4=8
A:23+8+4=35
H:53+3+28=84
I:11+17+93=121
I:24+8+3=35
I think that is all correct
FIND THE SUM OF ALL NATURAL NUMBERS FROM 1 TO 100 (ARITHMETIC PROGRESSION)
Answer:
According to arithmetic progression, natural numbers can be written down as 1, 2, 3, 4, 5, 6, 7, and 8 to 100. Basically, the sum of the first 100 natural numbers is equal to 5050.
You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2?
In scenerio 1, the money in the retirement account at 62 years old is $1,267,250.76
In scenerio 2, the money in the retirement account at 62 years old is $ 633,625.38.
How do we calculate future value of an ordinary annuity?Scenerio 1:
a) 6% of salary = Salary * 6% = $6,100 * 6% = $366
b) Total amount the company paid monthly = 6% of salary = Salary * 6% = $6,100 * 6% = $366
c) The money in the retirement account at 62 years old can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where:
FV = Future value = Money in the retirement account at 62 years old = ?
M = Monthly payment = Contribution you + Contribution by the employer = $366 + $366 = $732
r = Monthly interest rate = Annual interest rate / 12 = 6.28% / 12 = 0.0628 / 12 = 0.0052
n = number of months = Number years * Number of months in a year = (Retirement age – Age when hired) * 12 = (62 - 25) * 12 = 37 * 12 = 444
Substituting all the values into equation (1), we have:
FV = $732 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $1,267,250.76
d) Amount of money you put into the account = 6% of salary * number of months = $366 * 444 = $162,504
e) Amount of money your employer put into your account = Amount of money you put into the account = $162,504
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $1,267,250.76 – ($162,504 + $162,504) = $942,242.76
Scenario 2:
a) 3% of salary = Salary * 3% = $6,100 * 3% = $183
b) Total amount the company paid monthly = 3% of salary = Salary * 3% = $6,100 * 3% = $183
c) Using equation (1), we have:
M = Monthly payment = Contribution you + Contribution by the employer = $183 + $183 = $366
Substituting all the values into equation (1), we have:
FV = $366 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $633,625.38
d) Amount of money you put into the account = 3% of salary * number of months = $183 * 444 = $81,252.00
e) Amount of money your employer put into your account = Amount of money you put into the account = $81,252
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $633,625.38 – ($81,252 + $81,252) = $471,121.38
The difference in the amount of money at age 62 between scenarios 1 and 2 = Money in the retirement account at 62 years old in scenarios 1 + Money in the retirement account at 62 years old in scenarios 2 = $1,267,250.76 - $633,625.38 = $633,625.38
Difference in the amounts of money you put into retirement between scenarios 1 and 2 = $366 - $183 = $183
Amount got from your employer in scenario 1 than 2 = $366 - $183 = $183
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a wall in marcus's bedroom is 8 2/25 feet high and 16 2/3 long. If he paints 1/2 the wall blue how many square feet will be blue
Answer: 66.70
Step-by-step explanation:
8 2/25 times 16 2/3 then divide by 2 and you get 66.70 will be blue
Identify the range of the function shown in the graph.
the range of the function shown in the graph -1 [tex]\leq[/tex] y[tex]\leq[/tex] 1.
What is the sine and cosine graph's range?All real numbers fall within the domain of the sine and cosine functions. Both the sine and cosine functions have a range of [1,1]. An angle's sine and cosine have the same absolute value as their respective reference angles.
What is a cosine graph's range?An illustration of the function's range in the graphs of cos and sine
The cosine function's graph appears as follows: The range of the function y=cos(x) is 1y1, and the domain is all real numbers (cosine is defined for any angle measure).
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Please help if you can or and know how to do this pls! Can
Answer:
m<1=50
m<2=130
m<3=50
m<4=130
m<5=40
m<6=40
m<7=90
m<8=140
Step-by-step explanation:
The points (-5, 5) and (5, u) fall on a line with a slope of 3/10 What is the value of u?
Thank you!
Answer:
u = 8
Step-by-step explanation:
calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )
m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives
[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )
10(u - 5) = 30 ( divide both sides by 10 )
u - 5 = 3 ( add 5 to both sides )
u = 8
Step-by-step explanation:
(u - 5)/(5 + 5)= 3/10
(u - 5)/10= 3/10
10u - 50 = 30
10u = 80
u = 8
If the radius of a spherical orange is 3.5 cm. find its surface area and volume
Answer:
The surface area of a sphere is given by the formula:
surface area = 4 * pi * r^2
Where r is the radius of the sphere.
Using this formula, the surface area of an orange with a radius of 3.5 cm is:
surface area = 4 * pi * (3.5 cm)^2
= 4 * pi * 12.25 cm^2
= 49.0307 cm^2
The volume of a sphere is given by the formula:
volume = (4/3) * pi * r^3
Where r is the radius of the sphere.
Using this formula, the volume of an orange with a radius of 3.5 cm is:
volume = (4/3) * pi * (3.5 cm)^3
= (4/3) * pi * 42.875 cm^3
= 113.097 cm^3
Step-by-step explanation:
Given ,
Radius of a spherical orange is 3.5 cmTo Find : The Surface Area and the volume of a spherical orange
In order to find the surface area of a spherical orange we use the formula,
[tex]SA = 4\pi r^{2}[/tex]
[tex]SA = 4X\frac{22}{7} X 3.5X3.5[/tex]
[tex]SA =[/tex] [tex]154cm^{2}[/tex]
And now to find the volume of a sphere
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
[tex]V = \frac{4}{3} X \frac{22}{7} X (3.5)^{2}[/tex]
[tex]V[/tex] [tex]= 179.59cm^{2}[/tex]
Hence, the surface area is 154[tex]cm^{2}[/tex]and the volume of a sphere is [tex]179.59cm^{2}[/tex]
Math
A 6. 0 kg bowling ball traveling at 2 m/s strikes a 1. 5 kg bowling pin. Describe and compare the forces that act on the bowling ball and the bowling pin
during the collision.
By using formula and solving, Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t
What is collision?A collision is an event in which two or more objects come into contact with each other. In physics, a collision is defined as a rapid and forceful interaction between two or more objects that causes a transfer of energy. Collisions can be elastic or inelastic, depending on whether or not the total kinetic energy of the objects is conserved.
What is force?Force is a physical quantity that describes the interaction between two or more objects. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause an object to accelerate, change its shape, or change its direction of motion. Forces can be categorized into different types, such as contact forces, which act when two objects are in contact, and non-contact forces, which act at a distance. Some examples of non-contact forces are gravitational force, electric force, and magnetic force.
To calculate the force of impact on the bowling ball and bowling pin during the collision, you can use the formula:
Force of Impact = Change in momentum / Time of collision
The change in momentum is given by the formula:
Change in momentum = Final momentum - Initial momentum
The initial momentum of the 6 kg bowling ball traveling at 2 m/s is:
Initial momentum (ball) = 6 kg * 2 m/s = 12 kg*m/s
The final momentum of the bowling ball can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision. In this case, since the bowling pin is moving after the collision and the bowling ball is not, the final momentum of the bowling ball is zero.
Final momentum (ball) = 0
Change in momentum (ball) = Final momentum (ball) - Initial momentum (ball) = 0 - 12 kgm/s = -12 kgm/s
The force of impact on the bowling ball is:Force of impact (ball) = Change in momentum (ball) / Time of collision = -12 kg*m/s / t (t is the time of collision, assuming it's a short time)
Similarly, the initial momentum of the 1.5 kg bowling pin at rest is:
Initial momentum (pin) = 1.5 kg * 0 m/s = 0 kg*m/s
The final momentum of the bowling pin can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision.
Final momentum (pin) = Initial momentum (ball) = 12 kg*m/s
Change in momentum (pin) = Final momentum (pin) - Initial momentum (pin) = 12 kgm/s - 0 kgm/s = 12 kg*m/s
The force of impact on the bowling pin is:
Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t
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What are the 15 types of angles?
There are various classifications of angles, some of which include: Acute angles, Right angles, Obtuse angles, Straight angles, Reflex angles, Complementary angles, Supplementary angles, Adjacent angles, Linear pair, Vertically opposite angles, Alternate interior angles, Alternate exterior angles, Corresponding angles, Conjugate angles, and Explementary angles.
It's important to note that this is not an exhaustive list and the classification may vary depending on the context.
Acute angles which measure less than 90 degrees, Right angles that measure exactly 90 degrees, Obtuse angles that measure more than 90 degrees but less than 180 degrees.
There is also Straight angles that measure exactly 180 degrees, Reflex angles that measure more than 180 degrees but less than 360 degrees, Complementary angles which add up to 90 degrees, Supplementary angles which add up to 180 degrees.
Then there is Adjacent angles that share a common vertex and a common side but no common interior points, Linear pair which add up to 180 degrees and share a common side, Vertically opposite angles that are formed by two intersecting lines and are opposite to each other, Alternate interior angles that are formed by two intersecting lines on opposite sides of a transversal and inside parallel lines, Alternate exterior angles that are formed by two intersecting lines on opposite sides of a transversal and outside parallel lines, Corresponding angles that are formed by two intersecting lines in the same relative position.
Conjugate angles are angles which are supplementary but non-adjacent, and Explementary angles are angles which add up to 90 degrees.
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The roof on a house is 6 metres wide peaks at at a height of 3 metres above the top of the walls. Find the length of the sloping side of the roof.
Consider the inequality X-3/6< x/4 -4. Which value of x is a solution to the inequality?
A.x=-10
B.x=-5
C.x=5
D.x=10
x=5 is the value of the x that is the solution of the given inequality.
Define inequality.Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
What are types of inequality.>,< and not equal to are types of inequality.
x=5 is the value of the x that is the solution of the given inequality.
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Please help me with my HW
Answer:
24d^5
Step-by-step explanation:
At a coffee shop, the first 100
customers' orders were as follows.
Small
Medium
Large
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered a
hot drink given that he or she ordered a large?
P( Hot Large ) = [?]
Round to the nearest hundredth
Answer:
0.07
Step-by-step explanation:
lets make a chart first
small | medium | large
hot | 5 | 48 | 22
cold | 8 | 1 | 5
1. add all the hot drinks
5+48+22=75
2. find 5/75,
5/75=0.0666666
The pitchers for the home team had 12 strikeouts for 32 batters, while the pitchers for the visiting team had 15 strikeouts for 35 batters. Which pitching team had a greater fraction of strikeouts.(Hint: Just make the 12 for 32 and 15 for 35 into fractions and see which is greater or less than.)
Answer:
2958843/5 5/1000775747373838388484737372737375823A coin is tossed, a number cube is rolled, and a letter is picked from the word framer. 10. P(tails, 5, m)
Answer: The function you provided describes an experiment in which a coin is tossed, a number cube is rolled, and a letter is picked from the word "framer". The outcome of the experiment is represented by the ordered triple (tails, 5, m).
P(tails, 5, m) refers to the probability of the outcome (tails, 5, m) occurring. To find this probability, you would need to know the probability of each individual event:
The probability of getting tails is 1/2,
The probability of getting a 5 on a number cube is 1/6
and probability of getting letter "m" in the word "framer" is 1/6
So P(tails, 5, m) = (1/2) * (1/6) * (1/6) = 1/72
It is to be noted that in order for the inverse function to exist, the function must be one-to-one, meaning each y value has one unique x value, meaning the random variables in question should be independent. But in this case the events are dependent on one another.
Step-by-step explanation:
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
Define arithmetic mean.When all of the values in a set of data have the same unit of measurement, such as when all of the numbers are heights, miles, hours, etc., this technique is utilized. Take the numbers 4, 7, 9, and 10 as an illustration. The count of numerals is 4, and the sum of the numbers is 30. 30 divided by 4 equals 7.5, which is the numbers' arithmetic mean.
Here,
Given that there is a common difference between each word, this is an arithmetic sequence. In this instance, the following term is obtained by adding 9 to the phrase before it in the sequence.
Alternatively put,
=> an=a1+d(n−1)
.Arithmetic Sequence:
d=9
This is the formula of an arithmetic sequence.
=>an=a1+d(n−1)
Substitute in the values of
=> a1 =4 and
d=9
.=>an=4+9(n−1)
Simplify each term.
Tap for more steps...
an=4+9n−9
Subtract 9 from 4
an=9n−5
Thus 30th term :
=> a(30)=9(30)−5
=> a(30) = 265
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
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Work out the size angle BCD
By using the fact that the interior angles should add up to 360°, we will see that:
C = 142°
How to find the missing angle?We know that for any polygon of N sides, the sum of the interior angles is equal to:
S = (N - 2)*180°
In this case, the polygon has 4 sides, then:
S = (4 -2)*180° = 360°
Then we can write the equation:
A + B + C + D = 360°
Replacing the known angles we get:
68° + 43° + C + 107° = 360°
And now we can solve this for C.
C = 360° - 107° - 43° - 68°
C = 142°
That is the measure of the angle BCD.
Learn more about interior angles:
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