Question

In given figure, AB||CD||EF and GH||KL. The measure of angle HKL is.
(A)85 degrees
(B)135 degrees
(C)145 degrees
(D)215 degrees

Answer 1

Answer:

The measure of  ∠HKL is 145°.

Option (C)  145° is correct.

Step-by-step explanation:

Construction :  

Extend LK to meet line GF at point P.

From figure 8.127 ,  CD || EF,  

∠CHG =∠HGP = 60° [alternate angles are equal]

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

Hence, ∠KPG =180° – 60° = 120°

=> ∠GPK = ∠AKL = 120° [Corresponding angles are equal]

∠AKH = ∠KHD = 25° [alternate angles are equal]

Therefore, ∠HKL = ∠AKH + ∠AKL  

∠HKL = 25° + 120°  

∠HKL = 145°

Hence, The measure of  ∠HKL is 145°

Step-by-step explanation:

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