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 an isosceles trapezoid.

Step2: Use the property of adjacent angles in an isosceles trapezoid

In an isosceles trapezoid, adjacent angles along the non - parallel sides are supplementary. That is \(\angle A+\angle ADC = 180^{\circ}\)
Given \(\angle A=115^{\circ}\)
So, \(\angle ADC=180^{\circ}-\angle A\)
Substitute \(\angle A = 115^{\circ}\) into the formula: \(\angle ADC=180^{\circ}- 115^{\circ}\)
\(\angle ADC = 65^{\circ}\)

Answer:

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