Question

In Fig. 8.136, if CP || DQ, then the measure of x is
A. 130°
B. 105°
C. 175°
D. 125°

Answer 1

Given : CP || BQ

From figure :  

∠B = 105° , ∠A = 25°  and ∠PCA = x°

Produce PC to E So, PE ‖ BQ and AB is transversal.

∠QBE = ∠CEA = 105° [Corresponding angles]

In ∆ECA ,  

By angle sum property :  

∠CEA + ∠ECA + ∠EAC = 180°

105° + ∠ECA + 25° = 180°

130° + ∠ECA = 180°

∠ECA = 180° - 130°

∠ECA = 50°

∠PCA + ∠ECA = 180° [Linear pair]

x + 50° = 180°

x = 180° - 50°

x = 130°

Hence , the measure of x is  130° .

Option (A) 130° is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

Similar questions :

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

A. 20°

B. 30°

C. 45°

D. 60°

https://brainly.in/question/15906429

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

A. 180 – w + z

B. 180 + w – z

C. 180 – w – z

D. 180 + w + z

https://brainly.in/question/15906428

Answer 2

Answer:

the answer is 130

please mark as BRAINLIEST