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Answer :

Let ABCD be a parallelogram in which we have,
∠A = ∠B

We know \(∠A + ∠B = 180^{\circ}\quad\) [Sum of adjacent angles = \(180^{\circ}\)]

\(∠A + ∠A = 180^{\circ}\)

\(\Rightarrow 2∠A = 180^{\circ}\)

\(\Rightarrow ∠A = 90^{\circ}\)

Thus, \(∠A =∠C = 90^{\circ} and ∠B = ∠D = 90^{\circ}\quad \)
[Opposite angles of a parallelogram are equal]

- 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.
- 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 \(\bar { AB } ∥ \bar { DC }\)
- 12.Find the measure of ∠P and ∠S if \(\bar { SP } ∥ \bar { RQ }\) in figure, is there any other method to find m∠P?)

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