Question

in quadrilateral abcd, ( mangle c = 101^{circ} ). determine ( mangle a ).

Explanation:

Step1: Recall the property of cyclic quadrilaterals

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

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

Given \(m\angle C = 101^{\circ}\), we substitute into the formula \(m\angle A=180^{\circ}-m\angle C\).
So, \(m\angle A = 180^{\circ}- 101^{\circ}\).

Answer:

\(m\angle A = 79^{\circ}\)