Worksheet on Exterior Angles of a Polygon

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

We know, the sum of all the exterior angles of a polygon having n sides is 360°. The questions are based on finding the sum of the exterior angles of a polygon and the number of sides of a polygon using the formula.

1. Find the number of sides of a regular polygon if each of its exterior angle is:

(a) 45°

(b) 60°

(c) 120°

(d) 40°  

2. Draw a regular pentagon whose exterior angles are p, q, r, s, t and each interior angle is k.

What is the measure of:

(a) each interior angle

(b) each exterior angle

3. Each interior angle of a polygon is five (5) times the exterior angle of the polygon. Find the number of sides.

4. Find the minimum interior angles and maximum exterior angles possible in a regular polygon. Give reasons to support your answer.

5. Find the exterior angle of a regular polygon of:

(a) 5 sides           

(b) 9 sides          

(c) 15 sides         

(d) 19 sides

6. The ratio between an exterior angle and the interior angle of a regular polygon is 1 : 2. Find:

(a) the measure of each exterior angle.

(b) the measure of each interior angle.

(c) the number of sides in the polygon.

7. The measure of the exterior angle of a hexagon is (3x – 4)°, (x + 4)°, (7x – 3)°, (8x – 1)°, (2x + 3)°, (9x + 1)°. Find the measure of each angle.

8. Is it possible to have a regular polygon each of whose exterior angle is 50°? Give reason to support your answer.

9. The ratio of the exterior and interior angle of a regular polygon is 2 : 3. Find the number of sides in the polygon.

10. The exterior angles of a hexagon are in the ratio 1 : 1 : 2 : 2 : 3 : 3. Find all the interior angles of the hexagon.

11. The sum of all the interior angles of a polygon is four times the sum of its exterior angles. Find the number of sides in the polygon. Also, find the measure of each exterior angle and each interior angles.

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

Answers:

1. (a) 8

(b) 6

(c) 3

(d) 9

2. (a) 108°

(b) 72°

3. 12

4. 60°, 120°

5. (a) 72°

(b) 40°  

(c) 24°  

(d) 18\(\frac{18}{19}\)°

6. (a) 60°

(b) 120°

(c) 6

7. 68°, 28°, 165°, 191°, 51° and 217°

8. No

9. 5

10. 150°, 150°, 120°, 120°, 90° and 90°

11. Number of sides = 10, exterior angle = 36° and interior angle = 144°

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