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Question
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
Options
100°
120°
110°
130°
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Solution
Let ABCbe isosceles triangle
Then
AB = AC
∠B = ∠C
Now it is given that vertex angle is 2 times the sum of base angles
⇒∠A = 2 ∠(B+ C)
⇒∠A = 2 ∠(∠B + ∠B ) (As ∠B = ∠C)
⇒∠A = 2 (2∠B)
⇒∠A = 4 ∠B
Now
∠A + ∠B + ∠C = 180° (Property of triangle)
4∠B + ∠B + ∠B = 180° (Since ∠A = 4∠B, and ∠B = ∠C )
6∠B = 180°
∠B = 30°
∠A = 4∠B
`= 4 xx 30°`
= 120°
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