Worksheet on Interior Angles of a Polygon

Practice the questions given in the worksheet on interior angles of a polygon.

We know, the sum of all the interior angles of a polygon is (n – 2) × 180°. The questions are based on finding the sum of the interior angles of a polygon using the formula.

1. Is it possible to have a polygon whose sum of the interior angles is:

(a) 720°

(b) 840°

(c) 1080°

(d) 620°               

(e) 22°

2. Is it possible to construct a polygon, the sum of whose interior angles is 20 right angles? If yes, find the number of sides of the polygon.

3. The angle of a hexagon are in the ratio 1 : 2 : 3 : 4 : 6 : 8. Find the measure of the smallest and the biggest angles.

4. One of the angle of a polygon is 100° and each of the other angles is 110°. Find the number of sides in the polygon.

5. The ratio of number two sides of two regular polygons is 3 : 4 and the ratio of the sum of their interior angles is 1 : 2. Find the number of sides of each polygon.

6. The four angle of a hexagon are 60°, 90°, 150° and 180° and the other two angles are equal. Find the measure of these equal angles.

7. The measure of four angles of a heptagon is equal and the measure of the other three angles is 120° each. Find the measure of unknown angles.

8. The four angle of a pentagon are equal and the fifth angle measure 140°. Find the measure of four equal angles.

9. The seven angle of an octagon are 132° each. Find the measure of the eighth angle.

10. The angles of a pentagon are x°, (x – 5)°, (x + 15)°, (3x – 44)° and (x – 70)°. Find x.

11. The angle of a pentagon are (x – 1)°, (x – 2)°, (x – 3)°, (x – 4)° and (x – 5)° . Find the value of x and the measure of all angles.

12. Four of the angles of a pentagon are equal. The fifth angle is 40°. Find the angles.

13. Each interior angle of a polygon is 150°. Find the sum of interior angles of a polygon which has half the number of sides of the given polygon.

Answers for the worksheet on interior angles of a polygon are given below to check the exact answers of the above questions.

Answers:

1. (a) Yes

(b) No

(c) Yes

(d) No

(e) No

2. Yes, 12

3. Smallest angle = 30° and biggest angle = 240°

4. 5

5. 3, 4

6. 120°

7. 135°

8. 100°

9. 156°

10. 92

11. 111°, 110°, 109°, 108°, 107° and 106°

12. 125°, 125°, 125°, 125° and 40°

13. 720°

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Worksheet on Interior Angles of a Polygon

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