Question

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 1

The correct option is B. 25°

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Answer 2

Given : From  Fig. 8.129, PQ || RS, ∠AEF = 95°, ∠BHS = 110° and ∠ABC = x°.  

To find : Then the value of x.

 

Solution :  

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

∠AGH + ∠HGB = 180° (Linear pair)

95° + ∠HGB = 180°

∠HGB = 180° - 95°

∠HGB = 85°

∠BHS + ∠BHG = 180° (Linear pair)

110° + ∠BHG = 180°

∠BHG = 180° - 110°

∠BHG = 70°

In ∆BHG,

∠BHG + ∠HGB + ∠GBH = 180°

[By angle sum property]

70° + 85° + ∠GBH = 180°

155° + ∠GBH = 180°

∠GBH = 180° - 155°

∠GBH = 25°

Now,

∠ABC = ∠GBH = 25°

∠ABC = x° = 25°.

Hence, the value of x is 25°.

Option (B) 25° is correct.

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Some more questions :  

In Fig. 8.128, if AB||CD, then the value of x is

A. 20°

B. 30°

C. 45°

D. 60°

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In Fig. 8.130, if l1||l2, what is the value of x?

A. 90°

B. 85°

C. 75°

D. 70°

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