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Answer :

We have, \(∠Q = 130° and ∠R = 90^{\circ}\) and
\(\bar { SP } || \bar { RQ }\)

\(∠P + ∠Q = 180^{\circ}\quad\) [Adjacent angles]

\(\Rightarrow ∠P + 130^{\circ} = 180^{\circ}\)

\(\Rightarrow ∠P = 180^{\circ} – 130^{\circ} = 50^{\circ}\)

and also we have, \(∠S + ∠R = 180^{\circ}\quad\) [Adjacent angles]

\(\Rightarrow ∠S + 90^{\circ} = 180^{\circ}\)

\(\Rightarrow ∠S = 180^{\circ} – 90^{\circ} = 90^{\circ}\)

Hence, \(m∠P = 50^{\circ} \;and \; m∠S = 90^{\circ}\)

**Alternate Method:**

\(∠Q = 130^{\circ}, ∠R = 90^{\circ} and ∠S = 90^{\circ}\)

We know that

\(∠P + ∠Q + ∠R + ∠Q = 360^{\circ}\quad\) [Angle sum property of quadrilateral]

\(\Rightarrow ∠P + 130^{\circ}+ 90^{\circ} + 90^{\circ} = 360^{\circ}\)

\(\Rightarrow ∠P + 310^{\circ} = 360^{\circ}\)

\(\Rightarrow ∠P = 360^{\circ}– 310° = 50^{\circ}\)

Hence \(m∠P = 50^{\circ}\)

- 1.Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = ………… (ii) ∠DCB = ……… (iii) OC = ……… (iv) m?DAB + m∠CDA = ……..
- 2.Consider the following parallelograms. Find the values of the unknowns x, y, z.
- 3.Can a quadrilateral ABCD be a parallelogram if (i) \(∠D + ∠B = 180^{\circ}?\) (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii)\(∠A = 70^{\circ} and ∠C = 65^{\circ}?\)
- 4.Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
- 5.The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
- 6.Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
- 7.The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
- 8.The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
- 9.In the above figure both RISK and CLUE are parallelograms. Find the value of x.
- 10.Explain how this figure is a trapezium. Which of its two sides are parallel?
- 11.Find m∠C in below figure if \(\bar { AB } ∥ \bar { DC }\)

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