Q. 134.1( 15 Votes )

# In Fig. 8.127, *AB*||*CD*||*EF* and *GH*||*KL*. The measure of ∠*HKL* is

A. 85°

B. 135°

C. 145°

D. 215°

Answer :

Given,

AB ‖ CD ‖ EF and GH ‖ KL

Produce HG to M and KL to N

∠MHD and ∠CHG = 60^{o} (Vertically opposite angle)

Since,

MG ‖ NL and transversal cuts them

So,

∠MHD + ∠1 = 180^{o} (Interior angles)

60^{o} + ∠1 = 180^{o}

∠1 = 120^{o}

∠3 = ∠HKD = 25^{o} (Alternate angles) (i)

∠1 = ∠MKL = 120^{o} (Corresponding angles) (ii)

Now,

∠HKL = ∠3 + ∠MKL

= 25^{o} + 120^{o}

= 145^{o}

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