In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is
A. 100°
B. 120°
C. 110°
D. 130°
Answers
Given : In an isosceles triangle, if the vertex angle is twice the sum of the base angles.
Let, ABC be an isosceles triangle and each base angles be ∠B =∠C = x and Vertex angle be ∠A.
Vertex angle , ∠A = 2(x + x) 2x + 2x
∠A = 4x
We know that the sum of all the angles of a triangle is 180° :
∠A + ∠B + ∠C = 180°
4x + x + x = 180°
6x = 180°
x = 180°/6
x = 30°
So, ∠B = ∠C = 30°
Therefore, vertex angle ∠A = 4x = 120°
Hence , the measure of vertex angle of the triangle is 120° .
Option (B) 120° is correct.
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Answer:
Let, ABC be an isosceles triangle and each base angles be zB =<C = x and Vertex angle be ZA.
Vertex angle, ZA = 2(x + x) 2x + 2x
ZA = 4x
We know that the sum of all the angles of a triangle is 180° :
ZA + 2B + 2C = 180°
4x + x + x = 180°
6x = 180°
x = 180%6
x = 30°
So, <B= 2C = 30°