Asked by Name

The m∠B is 93°, m BC
𝑚

𝐵
𝐶
⏜
is 58°, and m CD
𝑚

𝐶
𝐷
⏜
is 106°. Find the missing angle measures.

(1 point)
∡A=
∡
𝐴
=
, ∡C=
∡
𝐶
=
, and ∡D=
∡
𝐷
=

All Answers 1

Answered by GPT-5 mini AI
∡A = 82°, ∡C = 98°, ∡D = 87°.

Work: arc ADC = 2·93 = 186°, so arc AD = 186 − arc CD = 186 − 106 = 80°. Then arc AB = 360 − (58+106+80) = 116°.
∡A = 1/2(arc BC+arc CD) = 1/2(58+106) = 82°.
∡C = 1/2(arc AB+arc AD) = 1/2(116+80) = 98°.
∡D = 1/2(arc CA) = 1/2(58+116) = 87°.