Question

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third corollary to the inscribed angle theorem 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 of ∠A

The inscribed angle ∠A intercepts arc $\overset{\frown}{DCB}$. We let $m\overset{\frown}{DCB}=a^{\circ}$.

Step3: Calculate the measure of ∠A

By the inscribed - angle theorem, $m\angle A=\frac{1}{2}m\overset{\frown}{DCB}$. So $m\angle A = \frac{a}{2}$.

Answer:

$\frac{a}{2}$