Question

A circle is centered on point BBB. Points AAA, CCC and DDD lie on its circumference. If \blue{\angle ABC}∠ABCstart color #6495ed, angle, A, B, C, end color #6495ed measures 40^\circ40 ∘ 40, degrees, what does \orange{\angle ADC}∠ADCstart color #ffa500, angle, A, D, C, end color #ffa500 measure?​

Answer 1

122°

The measure of the central angle is twice the measure of the inscribed angle that subtends the same arc.

∠ABC = 2×∠ADC = 2×61°

∠ABC = 122°

Explanation: