Question

The isosceles trapezoid is part of an isosceles triangle with a 26° vertex angle. What is the measure of an acute base angle of the trapezoid?

Answer 1

The angle of the trapezoid is 77 degrees

Answer 2

Answer:  The measure of an acute base angle of the trapezoid BPQC is 77°.

Step-by-step explanation:  As given in the question, the isosceles trapezoid BPQC is a part of the isosceles triangle ABC with same base BC. And, the vertex angle, m∠A = 26°.

We are to find the measure of an acute base angle of the trapezoid. That is, measure of angle B or angle C.

Since ΔABC is an isosceles triangle, so

$AB=BC\\\\\Rightarrow m\angle C=m\angle B.$

Now, using the angles sum property of a triangle, we have

$m\angle A+m\angle B+m\angle C=180^\circ\\\\\Rightarrow 26^\circ+m\angle B+m\angle B=180^\circ\\\\\Rightarrow 2m\angle B=154^\circ\\\\\Rightarrow m\angle B=77^\circ.$

So, m∠B = m∠C = 77°.

Thus, the measure of an acute base angle of the trapezoid BPQC is 77°.