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**Worksheet Question (Part - 1)****1.** What is the sum of all the interior angles of a polygon having â€˜nâ€™ sides?**2. **What is the sum of all the exterior angles of a polygon?**3.** What is the measure of an exterior angle of a regular octagon?**4. **What is the measure of an interior angle of a regular hexagon?**5.** If the exterior angle of a regular polygon is 72Â°, then what is the number of sides of the polygon?**6.** If the interior angle of a regular polygon is 144Â°, then what is the number of its sides?**ANSWERS****1.** (n â€“ 2) x 180Â°**2.** 360Â°**3. **45Â°**4.** 120Â°**5.** 5**6.** 10**Worksheet Question (Part - 2)****1.** In a parallelogram ABCD, if mâˆ A = 124Â°, then find the mâˆ B.**2.** PQRS is a parallelogram such that mâ€“R = 110Â°, then find mâ€“P and â€“S.**3. **Two opposite angles of a parallelogram are (5x â€“ 8)Â° and (2x + 82)Â°. Find the measures of each angle of the parallelogram.**4.** In the figure, find all the angles of the parallelogram ABCD, if mâ€“A : mâ€“B = 1 : 4.**5.** Find the perimeter of the parallelogram BCDE.**6.** In the figure, PQRS is a parallelogram. Find x, y and z.**7.** JKLM is a parallelogram. If mâ€“J = 70Â°, then find all other angles.**8.** In a parallelogram if measures of two adjacent angles are in the ratio of 4 : 5, find all the angles.**9.** ABCD is a parallelogram. Given than OC = 4 cm and DB is 5 cm more than AC, find OD.

10. If ABCD is an isosceles trapezium such that mâ€“CDA = 3x and mâ€“BAD = 2x. Find all angles of the trapezium.**ANSWERS**

**1.** 56Â°

**2.** mâˆ P = 110Â° and mâˆ S = 70Â°**3.** 142Â°, 38Â°, 142Â°, 38Â°**4.** 36Â°, 144Â°, 36Â°, 144Â°

**5. **38 cm**6.** x = 100Â°, y = 100Â°, z = 80Â°**7.** mâˆ M = 110Â°, mâˆ L = 70Â° and mâˆ K = 110Â°.**8.** 80Â°, 100Â°, 80Â°, 100Â°**9.** 6.5 cm**10.** 108Â°, 72Â°, 108Â°, 72Â°.**Worksheet Question (Part - 3)****1. Fill in the blanks:**

(i) The diagonals of a rhombus bisect each other at ________.

(ii) All angles of rectangle are equal and are ________ angles.

(iii) All sides of a ________ are equal and all angles are right angles.

(iv) A rhombus is a quadrilateral with ________ of equal length.

(v) A square has sides of equal length and angels of equal measure, so it is a ________ polygon.**2. Write â€˜Trueâ€™ or â€˜Falseâ€™ for each of the following:**

(i) Every rhombus is a square.

(ii) Every square is a rhombus.

(iii) Every rhombus is a rectangle.

(iv) Every rectangle is a rhombus.

(v) Every rhombus is a parallelogram.

(vi) Diagonals of a rhombus need not to be equal in length.

(vii) Every parallelogram is a rectangle.**ANSWERS****1.** (i) right angles

(ii) right

(iii) square

(iv) sides

(v) regular**2.** (i) False

(ii) True

(iii) False

(iv) False

(v) True

(vi) True

(vii) False

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