Question

The m∠B
𝑚
∠
𝐵
is 93°, mBC
𝑚
𝐵
𝐶
⏜
is 58°, and mCD
𝑚
𝐶
𝐷
⏜
is 106°. Find the missing angle measures.

(2 points)
m∠A=
𝑚
∠
𝐴
=
°, m∠C=
𝑚
∠
𝐶
=
°, and m∠D=
𝑚
∠
𝐷
=
°

Answer 1

m∠A = 82°, m∠C = 98°, m∠D = 87°.

Reason: The inscribed angle A intercepts arc BD, and arc BD = arc BC + arc CD = 58° + 106° = 164°, so m∠A = 1/2·164° = 82°. In a cyclic quadrilateral opposite angles sum to 180°, so m∠C = 180° − 82° = 98° and m∠D = 180° − m∠B = 180° − 93° = 87°.