Triangle ABC is isosceles with AB =BC . If angle B is twice the measure of angle A find the measure of all the angles of the triangle.

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Solution

The Criteria for a triangle to become Isoceles triangle. It has two equal sides and two equal angles. ---(1)

And The Basic Criteria In all Triangles is that Sum of all three angles should be = 180 ---(2)

We are taking Angle A =x and Angle C as same = x (Since it is said it in question that this triangle is isosceles with AB=BC)
Refer the Figure
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And then it is said that

Now since Angle A = x
And from question Angle B = 2×Angle A

Angle B = 2x

Now from (1)

x+x+2x=180°

4x = 180°

x = 45°

So Angle A = 45°
Angle B = 2× 45° = 90
And Angle C = 45°

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