Question

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given: a circle with inscribed quadrilateral abcd prove: ∠a and ∠c are supplementary. 1. let m\\(\stackrel{\frown}{dcb}\\)=a°. then m\\(\stackrel{\frown}{dab}\\)= 90 - a 180 - a 360 - a

Explanation:

Step1: Recall circle - arc property

The sum of the measures of the arcs of a circle is 360°. For an inscribed quadrilateral ABCD in a circle, the arcs intercepted by opposite angles are supplementary. The arc \(m\widehat{DCB}\) and \(m\widehat{DAB}\) are the arcs intercepted by opposite - angles \(\angle A\) and \(\angle C\).

Step2: Calculate the measure of arc \(m\widehat{DAB}\)

Since the sum of the measures of the arcs of a circle is 360°, if \(m\widehat{DCB}=a^{\circ}\), then \(m\widehat{DAB}=360 - a^{\circ}\).

Answer:

\(360 - a\)