Question

In the given figure, AC ⊥ CE and ∠A : ∠B : ∠C = 3 : 2 : 1, find the value of ∠ECD.

Answer 1

In the given figure, AC ⊥ CE and ∠A : ∠B:∠C = 3:2:1. We need to find the value of ∠ECD 

Since, 

 ∠A : ∠B:∠C = 3:2:1

Let, 

∠A = 3x

 ∠B = 2x

 ∠C = x

Applying the angle sum property of the triangle, in ΔABC, we get,

 ∠A + ∠B +  ∠C = 180°

3x + 2x + x = 180°

6x = 180°

`x = (180°)/6 `

`x = 30°`

 Thus,

 ∠A = 3x = 3(30°) = 90°

 ∠B = 2x = 2 (30°) = 60°

 ∠C = x = 30°

Further, BCD is a straight line. So, applying the property, “the angles forming a linear pair are supplementary”, we get,

 ∠C +  ∠ACE +  ∠ECD = 180°

 ∠EDC = 30° + 90° = 180°

 ∠ECD + 120° = 180°

 ∠ECD = 180° - 120°

 ∠ECD = 60°

Therefore, ∠ECD = 60°.