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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

What do you observe? It is clear from the above that the exterior angles of each polygon altogether
form a complete angle, i.e., 360°.

Hence, the sum of the exterior angles of every polygon is 360°.
360°
For a regular polygon of n sides, the measure of each exterior angle will be .
n
Or
If the exterior angle is known, then the number of sides of the regular polygon will be
360° .
measure of one exterior angle

Example 6: In the adjoining figure, find the measure of unknown angle x.
Solution: We have, the sum of the exterior angles of a polygon = 360° 90°

\ In the given figure,
50°
90° + 50° + 110° + x = 360°
x
x = 360° – 250° 110°
x = 110°

Thus, the value of the angle x is 110°.

Example 7: Find the exterior angle of a regular polygon of 10 sides.
Solution: Number of sides, n = 10

360°
We have, the measure of each exterior angle a regular polygon of n sides =
n
360°
\ The measure of each exterior angle of a decagon (n = 10) = = 36° .
10
Example 8: The measure of each exterior angle of a regular polygon is 120°. Find the number of
sides of the polygon and also, write the name of the polygon.
Solution: The measure of each exterior angle of the regular polygon = 120°. [Given]

We have, the number of sides of a regular polygon
 360 ° 
360° 360°  Hint: n = 
= = = 3  exterior angle
measureofone exteriorangle 120°
Thus, the number of sides is 3, so it is an equilateral triangle.

Example 9: Find the measure of an interior angle and an exterior angle of a regular polygon of 9
sides.
( n − ) × 180 °
2
Solution: The measure of each interior angle of a regular polygon of n sides =
n
( 92) × 180°
−
\ The measure of each interior angle of the regular nonagon (n = 9) =
9
×
7 180°
= = 140°
9
And, the measure of an exterior angle of the nonagon = 180° – 140° = 40°.

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