In the diagram, mZJ = 39.59. Find mJK.
H
K
a. MJK 101°
b. JK = 799
C.
JK = 140.5°
JK = 50.5°
d.

Answer:

a) 101°

Step-by-step explanation:

arc HK = 2(39.59°) = 79.18°

arc JH = 180°

arc JK = 360° - 180° - 79.18° = 100.82°

JK = 101°

The correct answer is option (A) 101°

"It is an angle in a circle formed by two chords that have a common end point on the circle."

For given example,

m ∠J = 39.59°

We know, the measure of an inscribed angle in a circle equals half the measure of its intercepted arc.

⇒ m(∠J) = (1/2) × arc KH

⇒ arc KH = 2 × 39.59°

⇒ arc KH = 79.18°

Also, arc HJ = 180°

We know for given figure,

⇒ arc JK + arc KH +arc HJ = 360°

⇒ arc JK + 79.18° + 180° = 360°

⇒ arc JK + 259.18° = 360°

⇒ arc JK = 100.82°

⇒ mJK ≈ 101°

Therefore,  mJK = 101°

The correct answer is option (A) 101°

Learn more about the inscribed angle here:

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