# Find the measure of ∠P and ∠S if SP || RQ in Fig 3.34. (If you find m∠R , is there more than one method to find m∠P?)

**Solution:**

Given SP is parallel to RQ and SR is the traversal drawn to these lines. Hence, SPQR is a trapezium.

∠S + ∠R = 180°

∠S + 90° = 180° [Since, ∠R = 90° in the given figure]

∠S = 180° - 90°

∠S = 90°

Using the angle sum property of a quadrilateral,

∠S + ∠P + ∠Q + ∠R = 360°

90° + ∠P + 130° + 90° = 360°

∠P + 310° = 360°

∠P = 360° - 310°

∠P = 50°

Alternate Method:

∠P + ∠Q = 180° (adjacent angles with SP || RQ )

∠P + 130° = 180°

∠P = 180° - 130°

∠P = 50°

Also,

∠S + ∠R = 180° (adjacent angles)

∠S + 90° = 180°

∠S = 180° - 90°

∠S = 90°

**☛ Check: **Class 8 Maths NCERT Solutions Chapter 3

**Video Solution:**

## Find the measure of ∠P and ∠S if SP is parallel to RQ in the below figure. (If you find m∠R , is there more than one method to find m∠P?)

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 Question 12

**Summary:**

The measure of ∠P and ∠S if SP is parallel to RQ in the below figure is ∠S = 90° and ∠P = 50°.

**☛ Related Questions:**

- The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
- The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
- In the above figure both RISK and CLUE are parallelograms. Find the value of x.
- Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)

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