**In the figure not drawn to scale, PQRS is a parallelogram, PX = PY and YXQ is a straight line. Find(a) Angle PQY(b) Angle YPS**

**Solution**

(a) Find Angle PQY

Angle QPS + Angle PSR = 180 degrees because PQRS is a parallelogram.

Therefore, Angle SPQ = 180 degrees – 125 degrees = 55 degrees.

Angle PQY = 180 degrees – 95 degrees – Angle SPQ

= (180 – 95 – 55) degrees = 30 degrees

**Answer: Angle PQY is 30 degrees.**

(b) Find Angle YPS

Angle SPX = Angle SPQ – Angle QPX

= 55 degrees – 32 degrees

= 23 degrees

Angle PXY = 180 degrees – 95 degrees – Angle SPX

= (180 – 95 – 23) degrees

= 62 degrees

Angle PYX is also 62 degrees because triangle PYX is an isosceles triangle.

Angle PZY = (180 – 95) degrees = 85 degrees

Angle YPS = 180 degrees – Angle PZY – Angle PXY

= (180 – 85 – 62) degrees

= 33 degrees

**Answer: Angle YPS is 33 degrees.**

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