Question

The isosceles trapezoid is part of an isosceles triangle with a 36° vertex angle. What is the measure of an acute base angle of the trapezoid? What is the measure of an obtuse base angle of the trapezoid? The diagram is not drawn to scale

Answer 1

The answer is D) 72, 108

First you have to find out the measure of the two other angles in the triangle. Those two angles will be equivalent.

Because the sum of all three angles in a triangle is 180, you subtract 36 from it (180 - 36 = 144) then divide by 2 (144/2 = 72).

So, the two angles at the bottom of the triangle are each 72. Because those angles are supplementary to the angles at the top of the trapezoid, you subtract 72 from 180 (180 - 72 = 108).

108 + 108 = 216

The sum of all the angles in a trapezoid is 360, so subtract 216 from 360 (360 - 216 = 144) then divide by 2 (144/2 = 72)