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

Question

In Fig. 8.129, PQ ++ RS , &#x2220; AEF =95&#xB0;, &#x2220; BHS =110&#xB0; and &#x2220; ABC = x &#xB0;. Then the value of x is,

Philoid · Accepted 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