In the given figure, if PQ ⊥ PS, PQ || SR, ∠SQR = 28º and ∠QRT = 65º, then find the values of x and y. - Mathematics

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In the given figure, if PQ ⊥ PS, PQ || SR, ∠SQR = 28º and ∠QRT = 65º, then find the values of x and y.

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Solution

It is given that PQ || SR and QR is a transversal line.

∠PQR = ∠QRT (Alternate interior angles)

x + 28º = 65º

= 65º − 28º

x = 37º

By using the angle sum property for ΔSPQ, we obtain

∠SPQ + x + y = 180º

90º + 37º + y = 180º

y = 180º − 127º

= 53º

∴x = 37º and y = 53º

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Chapter 6: Lines and Angles - Exercise 6.3 [Page 108]

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NCERT Mathematics Class 9
Chapter 6 Lines and Angles
Exercise 6.3 | Q 5 | Page 108

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