Question

MATHEMATICS
5. In Fig. 6.43, if PQ-1 PS, PQ || SR, 2 SQR = 28° and LORT=65°, then find the values
of x and y.
P
95°
400
289
R
T
750
699
1-
R
Fig. 6.42
Fig. 6.43​

Answer 1

Answer:

Given: PQ is perpendicular to PS, PQ parallel SR, ∠SQR = 28° and, ∠QRT = 65°

To Find: Values of x and y

Proof : according to the question,

x + ∠SQR = ∠QRT (Alt. angles are equal)

x + 28° = 65°

x = 37°

Now,

In Δ PQS,

As we know that sum of int. angles of a triangle = 180°

=>∠ PQS + ∠ PSQ + ∠ QPS = 180°

Therefore,

=> y + 37° + 90° = 180°

=> y= 180° - 127°

=> y = 53°

So x=37° and y= 53°

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