Question

In Fig., PQ+RS, ∠AEF = 95°, ∠BHS = 110° and ∠ABC = x°. Then the value of x is,

A. 15°

B. 25°

C. 70°

D. 35°

Answer 1

Given that,

PQ ‖ RS

∠AEF = 95°

∠BHS = 110°

∠ABC = x°

∠AEF = ∠AGH = 95°(Corresponding angles)

∠AGH + ∠HGB = 180°(Linear pair)

95° + ∠HGB = 180°

∠HGB = 85°

∠BHS + ∠BHG = 180°(Linear pair)

110° + ∠BHG = 180°

∠BHG = 70°

In BHG,

∠BHG + ∠HGB + ∠GBH = 180°

70° + 95° + ∠GBH = 180°

∠GBH = 25°

Thus,

∠ABC = ∠GBH = 25°