Question

In Fig. 6.43, if PQI PS, PQII SR, 2 SQR = 28º and Z QRT= 65°, then find the values
of x and y​

Answer 1

PQS+SQR=QRT

x+28°=65°

x=65°-28°

x=37°

PQS+QPS+PSQ=180°

x+90°+y=180°

37°+90°+y=180°

y=180°-37°-90°

y=53°

Answer 2

Given :

• PQ is perpendicular to PS
• PQ // SR
• ∠SQR = 28°

To Find :

• Value of x and y.

Solution :

$\longmapsto\tt{x+28\degree=65\degree\:(Exterior\:angle)}$

$\longmapsto\tt{x=65\degree-28\degree}$

$\longmapsto\tt\bold{x=37\degree}$

In Δ PQS :

$\longmapsto\tt{\angle{PQS}+\angle{PSQ}+\angle{QPS}=180\degree\:(A.S.P)}$

$\longmapsto\tt{37\degree+y+90\degree=180\degree}$

$\longmapsto\tt{y+127\degree=180\degree}$

$\longmapsto\tt{y=180\degree-127\degree}$

$\longmapsto\tt\bold{y=53\degree}$

Therefore :

$\longmapsto\tt\bold{Value\:of\:x=37\degree}$

$\longmapsto\tt\bold{Value\:of\:y=53\degree}$