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
[tex]AB=BC\\\\\Rightarrow m\angle C=m\angle B.[/tex]
Now, using the angles sum property of a triangle, we have
[tex]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.[/tex]
So, m∠B = m∠C = 77°.
Thus, the measure of an acute base angle of the trapezoid BPQC is 77°.
