Question

GHJK is a rectangle. GH = HI and ∠HKJ = 50°. HLK and GLI are straight lines. Find ∠GLK.

(a) 100°

(b) 130°

(c) 95°

(b) 135°

Answer 1

Correct option is (c) 95°

∠GKL = ∠GKJ − ∠HKJ

∠GKL = 90^∘ − 50^∘ (Since, GKJH is a rectangle)

∠GKL = 40^∘

Now, in △GHI:

∠GHI = 90^∘

and, GH = HI

Thus, ∠HGI = ∠HIG (Isosceles triangle property)

Hence, ∠HGI = \(\frac 12\)​(180^∘−∠GHI)

∠HGI = 45^∘

Now, ∠KGL = ∠G − ∠HGI

∠KGL = 90^∘ − 45^∘

∠KGL = 45^∘

Now, In △GKL

∠GKL + ∠GLK + ∠LGK = 180^∘

40^∘ + ∠LGK + 45^∘ = 180^∘

∠GLK = 95^∘