Question

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corollary to the inscribed angle theorem
given: a circle with inscribed quadrilateral abcd
prove: ∠a and ∠c are supplementary.
√1. let m∠dcb = a°
then m∠dab = 360 - a√.
√2. by the inscribed angle theorem, m∠a = a/2√.

1. also by the inscribed angle theorem, m∠c =

Explanation:

Step1: Recall inscribed - angle theorem concept

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

Step2: Analyze arc - angle relationship for \(\angle C\)

The arc intercepted by \(\angle C\) is the arc \(DAB\). We know that \(m\overset{\frown}{DAB}=360 - a\). By the inscribed - angle theorem, \(m\angle C=\frac{m\overset{\frown}{DAB}}{2}\).

Step3: Calculate \(m\angle C\)

Substitute \(m\overset{\frown}{DAB}=360 - a\) into the formula for \(m\angle C\). So \(m\angle C=\frac{360 - a}{2}\).

Answer:

\((360 - a)/2\)