Question

In ΔABC, AB = BC. ∠A : ∠B = 2 : 1.

∴ find ∠B.

Options

• 30°

• 36°

• 45°

• 50°

Answer 1

36°

Explanation:

Given:

AB = BC Triangle is isosceles with equal sides AB and BC.

So, angles opposite these equal sides are also equal ∠C = ∠A.

Also given: ∠A : ∠B = 2 : 1.

Let ∠A = 2x, ∠B = x.

Since AB = BC, ∠A = ∠C = 2x.

Use the angle sum property of triangle:

∠A + ∠B + ∠C = 180°

Substitute values:

2x + x + 2x = 180°

5x = 180°

⇒ x = 36°

Therefore, ∠B = 36°.