In figure 9.36, AC ⊥ CE and ∠A:∠B: ∠C = 3: 2: 1, find

∠A: ∠B: ∠C = 3: 2: 1

Let the angles be 3x, 2x and x

⇒ 3x + 2x + x = 180° [Angle sum property]

⇒ 6x = 180°

⇒ x = 30° = ∠ACB

∴ ∠ECD = 180° − ∠ACB − 90° [Linear pair]

= 180° − 30° − 90°

= 60°

∴ ∠ECD = 60°