Question

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

Explanation:

Step1: Identify the quadrilateral type

The markings on the sides suggest it is an isosceles trapezoid where $AB\parallel CD$ and $AD = BC$. In an isosceles trapezoid, base - angles are equal. $\angle A$ and $\angle D$ are adjacent angles along a non - parallel side.

Step2: Use the property of adjacent angles in a trapezoid

Adjacent angles along a non - parallel side of a trapezoid are supplementary, that is $\angle A+\angle D = 180^{\circ}$. Given $\angle A=115^{\circ}$.
Let $\angle D=x$. Then $115^{\circ}+x = 180^{\circ}$.
Solve for $x$: $x=180^{\circ}- 115^{\circ}=65^{\circ}$.

Answer:

$65^{\circ}$