In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then what is the measure of vertex angle of the triangle?

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10°

12°

100°

120°

answer is D.

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Detailed Solution

Given, in an isosceles triangle, if the vertex angle is twice the sum of the base angles.
Let each base angle be x in an isosceles

△ ABC

.
Then the vertex angle is 2(x + x) = 4x.
By using the angle sum property of the triangle, 4x + x + x = 180°.

\Rightarrow

x = 30°
Thus, the vertex angle of the triangle is 4x i.e, 4(30) = 120°.
Hence, option 4 is correct.

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