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°

Answer 1

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°