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Answer :

We have, \(∠y = 40^{\circ}\) (Alternate angles)

\(∠z + 40°^{\circ} = 70^{\circ}\) (Exterior angle property)

\(\Rightarrow ∠z = 70^{\circ} – 40^{\circ} = 30^{\circ}\)

\(z = ∠EPH \quad\)[Alternate angle]

In ∆EPH,
\(∠x + 40^{\circ} + ∠z = 180^{\circ}\quad\) [Adjacent angles]

\(\Rightarrow ∠x + 40^{\circ} + 30^{\circ} = 180^{\circ}\)

\(\Rightarrow ∠x + 70^{\circ} = 180^{\circ}\)

\(\Rightarrow ∠x = 180^{\circ} – 70^{\circ} = 110^{\circ}\)

Hence we have,\( x = 110^{\circ}, y = 40^{\circ} and\; z = 30^{\circ}.\)

- 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.
- 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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