In Fig., AC perpendicular to CE and C ∠A: ∠B: ∠C= 3: 2: 1. Find

1.	In Fig., AC perpendicular to CE and C ∠A: ∠B: ∠C= 3: 2: 1. Find the value of ∠ECD.
Answer» In the given triangle, the angles are in the ratio 3: 2: 1. Let the angles of the triangle be 3x, 2x and x. We know that sum of angles in a triangle is 180° 3x + 2x + x = 180° 6x = 180° x = 30° Also, ∠ACB + ∠ACE + ∠ECD = 180° x + 90° + ∠ECD = 180° (∠ACE = 90°) We know that x = 30° Therefore ∠ECD = 60°

In Fig., AC perpendicular to CE and C ∠A: ∠B: ∠C= 3: 2: 1. Find the value of ∠ECD.

Answer»

In the given triangle, the angles are in the ratio 3: 2: 1.

Let the angles of the triangle be 3x, 2x and x.

We know that sum of angles in a triangle is 180°

3x + 2x + x = 180°

6x = 180°

x = 30°

Also, ∠ACB + ∠ACE + ∠ECD = 180°

x + 90° + ∠ECD = 180° (∠ACE = 90°)

We know that x = 30°

Therefore

∠ECD = 60°