Question

In Fig 8.107, AB ||CD ||EF and GH ||KL. Find ∠HKL.

Answer 1

In Fig 8.107, AB ||CD ||EF and GH ||KL. Find ∠HKL.

∠HKL=  145°

Construction: Produce LK to meet GF at N.

Consider the attached figure while going through the following steps.

∠ CHG= ∠ HGN   (alternate angles)

∴ ∠ HGN =   60°

∠ HGN = ∠ LNF  (corresponding angles)  

∴  ∠ LNF =  60°

Therefore ∠ KNG=  180° - 60° = 120°

∠ GNK= ∠ AKL  (corresponding anlges)

∴  ∠ AKL =  120°

∠ AKH = ∠ KHD  (alternate angles)

∴ ∠ KHD =  25°

∠ HKL= ∠ AKH + ∠ AKL  

= 25° + 120°

∴ ∠ HKL = 145°