Question

In Fig. 9.39, AB||DE. Find ∠ACD.

Answer 1

In Fig. 9.39, AB||DE.  ∠ACD = 70°

Given,

AB ‖ DE

From figure it's clear that,

∠ABC = ∠CDE   (alternate angles)

∠ABC = 40°

In  Δ ABC

∠BAC + ∠ABC + ∠ACB = 180°

30° + 40° + ∠ACB = 180°

∠ACB = 180° - 70°

∴ ∠ACB  = 110° .........(1)

Now,

∠ACD + ∠ACB = 180° (Linear pair)

∠ACD + 110° = 180° [From  eqn (1)]  

∠ACD = 180° - 110°    

∴ ∠ACD = 70°

Hence, ∠ACD = 70°.