Question

The m∠B is 93°, m BC
is 58°, and m CD
is 106°. Find the missing angle measures.

(1 point)
∡A=

, ∡B=
, and ∡C=

Answer 1

If A, B, C, D lie on the circle in that order, an inscribed angle equals half the measure of its intercepted arc.

Angle B intercepts arc ADC, so arc ADC = 2·93° = 186°. Since arc CD = 106°, arc AD = 186° − 106° = 80°.

Angle A intercepts arc BC, so ∠A = 1/2·58° = 29°.

Arc AB = 360° − (arc BC + arc CD + arc DA) = 360° − (58° + 106° + 80°) = 116°, so ∠C = 1/2·116° = 58°.

Thus ∡A = 29°, ∡B = 93°, ∡C = 58°.