Question

In the given figure, AC ⊥ CE and ∠A : ∠B : ∠C = 5 : 3 : 2. The value of ∠ECD will be

Options

• 62°

• 45°

• 54°

• 30°

Answer 1

54°

Explanation:

As the ratio is ∠A : ∠B : ∠C = 5 : 3 : 2

⇒ ∠A = 5x, ∠B = 3x, ∠C = 2x

We know that,

∠A +∠B + ∠C = 180°

5x + 3x + 2x = 180°

10x = 18°

⇒ x = 18

∴ ∠A = 5 × 18 = 90°

∠B = 3 × 18 = 54°

∠C = 2 × 18 = 36°

Also, ∠ACD = ∠BAC + ∠ABC 

(∵ In any triangle exterior angle is equal to sum of opposite interior angles.)

⇒ ∠ACE + ∠ECD = 90° + 54°

90° + ∠ECD = 90° + 54°

⇒ ∠ECD = 54°