Question

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

Explanation:

Step1: Identify the quadrilateral type

From the markings (AB = CD, AD || BC, AB || CD? Wait, the markings: AB and CD have one mark, AD and BC have one mark? Wait, the diagram: AB and CD are marked with one tick, AD and BC with one tick? Wait, no, the arrows: AD and BC have arrows, meaning they are parallel. AB and CD have ticks, meaning they are equal in length. So ABCD is a parallelogram (since one pair of sides is parallel and equal, or both pairs of opposite sides parallel? Wait, AD || BC (arrows) and AB = CD (ticks), also AB and CD: if AD || BC and AB = CD, then it's a parallelogram. In a parallelogram, consecutive angles are supplementary.

Step2: Use supplementary angles in parallelogram

In parallelogram ABCD, angle at A (∠DAB) and angle at D (∠ADC) are consecutive angles, so they are supplementary. So ∠DAB + ∠ADC = 180°. Given ∠DAB = 115°, so ∠ADC = 180° - 115° = 65°.

Answer:

65° (corresponding to the option with 65°)