Question

given: a circle with inscribed quadrilateral abcd. prove: ∠a and ∠c are supplementary. 1. let mdcb = a°. then mdab = 360 - a. 2. by the inscribed - angle theorem, m∠a =

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc for ∠A

The inscribed angle ∠A intercepts arc $\overset{\frown}{DCB}$. We know that $m\overset{\frown}{DCB}=a^{\circ}$. According to the inscribed - angle theorem, $m\angle A=\frac{1}{2}m\overset{\frown}{DCB}$.

Answer:

$\frac{a}{2}$