Question

in quadrilateral abcd, m∠a = 72°. determine m∠c. enter the answer in the space provided. use numbers instead.

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the sum of opposite angles is \(180^\circ\). So, \(\angle A\) and \(\angle C\) are opposite angles.

Step2: Calculate \(m\angle C\)

Given \(m\angle A = 72^\circ\), using the property \(m\angle A + m\angle C = 180^\circ\), we solve for \(m\angle C\):
\(m\angle C = 180^\circ - m\angle A\)
Substitute \(m\angle A = 72^\circ\) into the formula:
\(m\angle C = 180 - 72 = 108^\circ\)

Answer:

\(108\)