Question

what is the measure of ∠adc in quadrilateral abcd? 45° 65° 115° 135°

Explanation:

Step1: Identify the type of quadrilateral

Since \(AB = CD\) and \(BC\parallel AD\), quadrilateral \(ABCD\) is a parallelogram.

Step2: Use the property of consecutive angles in a parallelogram

In a parallelogram, consecutive angles are supplementary. That is \(\angle A+\angle ADC = 180^{\circ}\).

Step3: Solve for \(\angle ADC\)

Given \(\angle A=115^{\circ}\), then \(\angle ADC=180^{\circ}-\angle A\). Substitute \(\angle A = 115^{\circ}\) into the formula: \(\angle ADC=180 - 115=65^{\circ}\)

Answer:

\(65^{\circ}\)