Question

In Fig. 8.128, if AB||CD, then the value of x is
A. 20°
B. 30°
C. 45°
D. 60°

Answer 1

Concept :  

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

 

Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

 

Given : AB ‖ CD  

Let, ∠1 = 120°  + x and ∠2 = x°

∠1 = ∠3 = 120° + x

[Alternate angles]

∠2 + ∠3 = 180°

[Linear pair]

x° + 120° + x = 180°

x° + x° + 120° = 180°

2x = 180° - 120°

2x = 60°

x = 60°/2

x = 30°

Hence , the  value of x is  30° .

Option (B) 30° is correct.

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

A. 90°

B. 85°

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In Fig. 8.131, if l1 || l2, what is x + y in terms of w and z?

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Answer 2

Answer:-

Concept :  

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

 

Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

 

Given :

AB ‖ CD  

Let, ∠1 = 120°  + x and ∠2 = x°

∠1 = ∠3 = 120° + x

[Alternate angles]

∠2 + ∠3 = 180°

[Linear pair]

x° + 120° + x = 180°

x° + x° + 120° = 180°

2x = 180° - 120°

2x = 60°

x = 60°/2

x = 30°

Hence , the  value of x is  30°

.

Option (B) 30° is correct.

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