Question

In the below fig, AB || CD || EF and GH || KL. Find `∠`HKL

Answer 1

Produce LK to meet GF at N.

Now, alternative angles are equal

`∠`CHG = `∠`HGN = 60° 

`∠`HGN = `∠`KNF = 60°          [Corresponding angles]

∴`∠`KNG = 180° - 60° = 120°

`∠`GNK = `∠`AKL = 120°                [Corresponding angles]

`∠`AKH = `∠`KHD = 25°                [Alternative angles]

∴`∠`HKL = `∠`AKH + `∠`AKL = 25° +120° = 145°.