Question

In Fig. 9.54, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR=25°, ∠RQC=30° and ∠CQF= 65°, then
A. x = 55°, y = 40°
B. x = 50°, y = 45°
C. x = 60°, y = 35°
D. x = 35°, y = 60°

Answer 1

Answer:

a) X= 55° Y=40°

Answer 2

Given: AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°.

 

 

To Find : The measure of x and y.

 

Proof :

We have AB ‖ CD

30° + 65° + ∠PQR = 180°

[Linear pair]

95° + ∠PQR = 180°

∠PQR = 180° - 95°

∠PQR = 85°

Since, AB ‖ DC and EF is a transversal and sum of the interior angles on the same side of a transversal is 180°.

∠APQ + ∠PQC = 180o  

(25° + y ) + (85° + 30°) = 180°

25° + y + 115° = 180°

140° + y = 180°

y = 180° - 140°

y = 40°

In ∆PQR,  

Since Sum of the angles of a triangle is 180° :  

∠PQR + ∠PRQ + ∠QPR = 180°

85° + x + y = 180°

85° + x + 40° = 180°

125° + x = 180°

x = 180° - 125°

x = 55°

Hence, x is 55°  and y is 40°.

Among the given options option (A) x = 55°, y = 40°  is correct.

 

HOPE THIS ANSWER WILL HELP YOU…..

 

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