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Question
In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is
Options
72°
73°
74°
95°
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Solution
It is given that
∠B = 2∠C,
AB = CD
∠BAD = DAC
∠ABE = ∠EBC
We have to find ∠BAC
Now AB = CD
AB = BD
Now the triangle is isosceles
∠B = 2∠C
Let
∠B = x
∠B = 2x
∠C = x
So ∠B = ∠A
Now
∠A + ∠B + ∠C = 180°
2x + 2x + x = 180°
5x = 180°
x = 36°
Since
∠A = 2x
= `2 xx 36°
= 72°
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