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Vera_Pavlovna [14]
3 years ago
6

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?

Mathematics
2 answers:
JulijaS [17]3 years ago
7 0
The angle of the trapezoid is 77 degrees
ICE Princess25 [194]3 years ago
6 0

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°.

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