Question

In Fig. 9.36, AC ⊥ CE and ∠A : ∠B :∠C = 3:2:1, find the value of ∠ECD.

Answer 1

The value of ∠ECD is 60°

Step-by-step explanation:

• Given data

        ∠A : ∠B :∠C = 3:2:1

        Let

        ∠A = 3k

        ∠B = 2k

        ∠C = k

• Now in Δ ABC , use triangle angle property

        ∠A +∠B+∠C = 180°

        3k + 2k + k = 180°

        6k = 180°

        k = 30°

• So

       ∠A = 3k =3×30° =90°

       ∠B = 2k =2×30° =60°

       ∠C = k =1×30° =30°

• Here BD is straight line, so

       ∠ACB +∠ACE+∠ECD = 180°     (It is given that ∠ACE is 90°)

       30° + 90° +∠ECD = 180°

      ∠ECD = 60°