Question

in quadrilateral abcd, ( mangle a = 72^{circ} ). determine ( mangle c ).

Explanation:

Step1: Use the property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\). So, \(m\angle A + m\angle C=180^{\circ}\).

Step2: Solve for \(m\angle C\)

Given \(m\angle A = 72^{\circ}\), then \(m\angle C=180^{\circ}-m\angle A\). Substitute \(m\angle A = 72^{\circ}\) into the formula: \(m\angle C = 180^{\circ}-72^{\circ}\).

Answer:

\(108^{\circ}\)