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in Lines and Angles by (38.0k points)
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In Fig., AB || CD || EF and GH || KL . The measure of ∠HKL is

A. 85°

B. 135°

C. 145°

D. 215°

1 Answer

+1 vote
by (36.4k points)
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Best answer

Given,

AB ‖ CD ‖ EF and GH ‖ KL

Produce HG to M and KL to N

∠MHD and ∠CHG = 60°(Vertically opposite angle)

Since,

MG ‖ NL and transversal cuts them

So,

∠MHD + ∠1 = 180°(Interior angles)

60° + ∠1 = 180°

∠1 = 120°

∠3 = ∠HKD = 25°(Alternate angles) (i)

∠1 = ∠MKL = 120°(Corresponding angles) (ii)

Now,

∠HKL = ∠3 + ∠MKL

= 25° + 120°

= 145°

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