Q. 175.0( 2 Votes )

# In Fig. 8.129, *PQ*++*RS*, ∠*AEF* =95°, ∠*BHS* =110° and ∠*ABC* =*x*°. Then the value of *x* is,

A. 15°

B. 25°

C. 70°

D. 35°

Answer :

Given that,

PQ ‖ RS

∠AEF = 95^{o}

∠BHS = 110^{o}

∠ABC = x^{o}

∠AEF = ∠AGH = 95^{o} (Corresponding angles)

∠AGH + ∠HGB = 180^{o} (Linear pair)

95^{o} + ∠HGB = 180^{o}

∠HGB = 85^{o}

∠BHS + ∠BHG = 180^{o} (Linear pair)

110^{o} + ∠BHG = 180^{o}

∠BHG = 70^{o}

In BHG,

∠BHG + ∠HGB + ∠GBH = 180^{o}

70^{o} + 95^{o} + ∠GBH = 180^{o}

∠GBH = 25^{o}

Thus,

∠ABC = ∠GBH = 25^{o}

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