Question

In the given figure, PQ || RS, AEF = 95°
BHS = 110° and ABC=xº. Find the value of x.
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Answer 1

Answer:

The value of x is 25°....

Answer 2

Step-by-step explanation:

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°.