Question

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

Explanation:

Step1: Identify the quadrilateral type

The quadrilateral \(ABCD\) is a parallelogram (opposite sides are parallel and equal).

Step2: Use the property of parallelograms

In a parallelogram, consecutive angles are supplementary. That is \(\angle A+\angle ADC = 180^{\circ}\).
Given \(\angle A=115^{\circ}\), then \(\angle ADC=180^{\circ}-\angle A\).
Substitute \(\angle A = 115^{\circ}\) into the formula: \(\angle ADC=180 - 115\).
\(\angle ADC = 65^{\circ}\)

Answer:

\(65^{\circ}\) (the second option)