Question

In the given figure, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.

Answer 1

Since, AE || BD and CH is a transversal.

∴∠CHE = ∠HCB – 120°  ......(i) [Alternate interior angles]

Now, CH || DF and CD is a transversal.

∴ ∠HCB =∠CDE  ......[Corresponding angles]

⇒ ∠CDE – 120°  ......(ii) [Using (1)]

Also, AB || DF and BD is a transversal.

∴ ∠ABC + ∠CDE = 180°  ......[Co-interior angles]

⇒ ∠ABC = 180° – 120°  ......[Using (ii)]

= 60°

Thus, ∠ABC = 60° and ∠CDE = 120°