Given PQ = 24
PS = 19
PR = 42
TQ = 10
m<PQR = 106°
m<QSR = 49°
m<PRS = 35°


find m<QRS, m<PQS, m<RPS and m<PSQ​

Given PQ = 24PS = 19PR = 42TQ = 10m&lt;PQR = 106m&lt;QSR = 49m&lt;PRS = 35find M&lt;QRS, M&lt;PQS, M&lt;RPS

Answers

Answer 1

The shape PQRS is a parallelogram

The measure of angle QRS is 70 degreesThe measure of angle PQS is 53 degreesThe measure of angle RPS is 35 degreesThe measure of angle PSQ is 53 degrees

The given parameters are:

[tex]\mathbf{\angle PQR = 106}[/tex]

[tex]\mathbf{\angle QSR = 49}[/tex]

[tex]\mathbf{\angle PRS = 35}[/tex]

(a) Find QRS

This is calculated as:

[tex]\mathbf{\angle QRS = 2 \times \angle PRS }[/tex]

So, we have:

[tex]\mathbf{\angle QRS = 2 \times 35}[/tex]

[tex]\mathbf{\angle QRS = 70}[/tex]

Hence, the measure of angle QRS is 70 degrees

(b) Find PQS

This is calculated as:

[tex]\mathbf{\angle PQS = \frac 12 \times \angle PQR }[/tex]

So, we have:

[tex]\mathbf{\angle PQS = \frac 12 \times 106}[/tex]

[tex]\mathbf{\angle PQS = 53}[/tex]

Hence, the measure of angle PQS is 53 degrees

(c) Find RPS

This is calculated as:

[tex]\mathbf{\angle RPS = \angle PRQ }[/tex]

Where:

[tex]\mathbf{\angle PRQ = \angle PRS = 35}[/tex]

So, we have:

[tex]\mathbf{\angle RPS = 35}[/tex]

Hence, the measure of angle RPS is 35 degrees

(d) Find PSQ

This is calculated as:

[tex]\mathbf{\angle PSQ =\frac 12 \times \angle PQR }[/tex]

Where:

[tex]\mathbf{\angle PSQ =\frac 12 \times \angle 106}[/tex]

So, we have:

[tex]\mathbf{\angle PSQ =53}[/tex]

Hence, the measure of angle PSQ is 53 degrees

Read more about angles in a parallelogram at:

https://brainly.com/question/12186483


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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Split

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[tex]\mathbf{MN = \frac{1}{2}AC}[/tex]

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[tex]\mathbf{\sqrt{29} = \frac{1}{2} \times 2\sqrt{29}}[/tex]

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Read more about midpoints and distance at:

https://brainly.com/question/11231122

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Step-by-step explanation:

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