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# In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that AD bisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is - Mathematics

MCQ

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°

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 12 Congruent Triangles
Q 20 | Page 88
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