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in Lines and Angles by (56.3k points)

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

1 Answer

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Best answer

Extend LK to meet line GF at point P.

From figure, CD || GF, so, alternate angles are equal. 

∠CHG =∠HGP = 60° 

∠HGP =∠KPF = 60° [Corresponding angles of parallel lines are equal] 

Hence, 

∠KPG =180 – 60 

= 120° 

∠GPK = ∠AKL= 120° [Corresponding angles of parallel lines are equal] 

∠AKH = ∠KHD = 25° [alternate angles of parallel lines] 

Therefore, ∠HKL = ∠AKH + ∠AKL 

= 25 + 120 

= 145°

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