Question

multiple - choice question

in the isosceles trapezoid above, find the measure of $\angle d$

$115^{circ}$

$65^{circ}$

rewatch

Explanation:

Step1: Recall properties of isosceles trapezoid

In an isosceles trapezoid, consecutive angles between the bases are supplementary. That is, \(\angle B+\angle A = 180^{\circ}\) and \(\angle C+\angle D=180^{\circ}\). Also, \(\angle A=\angle D\) (base angles of isosceles trapezoid are equal).

Step2: Calculate \(\angle D\)

Given \(\angle B = 115^{\circ}\). Since \(BC\parallel AD\), \(\angle B+\angle A=180^{\circ}\). Let \(\angle A = x\), then \(x + 115^{\circ}=180^{\circ}\), so \(x=\angle A=180^{\circ}- 115^{\circ}=65^{\circ}\).
Because in an isosceles trapezoid \(\angle A=\angle D\) (base - angle property of isosceles trapezoid), so \(\angle D = 65^{\circ}\)

Answer:

\(65^{\circ}\)