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 = a/2. 3. also by the inscribed - angle theorem, m∠c =

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 ∠C

The inscribed angle ∠C intercepts arc DAB. We know that \(m\widehat{DAB}=360 - a\).

Step3: Calculate m∠C

By the inscribed - angle theorem, \(m\angle C=\frac{m\widehat{DAB}}{2}\). Since \(m\widehat{DAB}=360 - a\), then \(m\angle C=\frac{360 - a}{2}\).

Answer:

\((360 - a)/2\)