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In Figure, if PQ ⊥ PS, PQ SR, SQR = 28° and QRT = 65°, then find the values of x and y.
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11/07/2021 11:23 am
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In Figure, if PQ ⊥ PS, PQ SR, SQR = 28° and QRT = 65°, then find the values of x and y.
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11/07/2021 11:25 am
x + SQR = QRT (As they are alternate angles since QR is transversal)
x + 28° = 65°
∴ x = 37°
It is also known that alternate interior angles are same and so,
QSR = x = 37°
QRS + QRT = 180° (As they are a Linear pair)
QRS + 65° = 180°
QRS = 115°
Now, we know that the sum of the angles in a quadrilateral is 360°
P + Q + R + S = 360°
Putting their respective values, we get,
S = 360°  90°  65°  115°
In Δ SPQ
∠SPQ + x + y = 180^{°}
90^{°} + 37^{°} + y = 180^{°}
y = 180^{°} – 127^{°} = 53^{°}
Hence, y = 53°
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