Question

Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = \[\frac{1}{2}\]∠A is equal to

Options

•  80°

•  75°

•  60°

•  90°

Answer 1

In the given problem, side BC of ΔABC has been produced to a point D. Such that ∠ACD  = 120° and `∠B = 1/2 ∠A` . Here, we need to find ∠A

Given `∠B = 1/2 ∠A`

We get,  ∠A = 2∠B  .........(1)

Now, using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,

In ΔABC

∠ACD = ∠A + ∠B

120° = 2∠B + ∠B

120° = 3∠B

`∠B = (120°)/3`

∠B = 40°

Also,  ∠A = 2∠B(Using 1)

∠ A = 2 (40°)

 = 80°

Thus, ∠A = 80°