Sum of the Measures of the Exterior Angles of a Polygon
Sum of the Measures of the Exterior Angles of a Polygon
In a polygon is the sides are produced in order we will get the exterior angles as shown below. The exterior angles are marked as A, B, C, D, E, F
Sum of exterior angles of a polygon for any number of sides = 3600
Regular Polygon:
A regular polygon is a polygon which has sides of equal length and all interior angles are also equal. All the exterior angles are also equal. So if there is a regular polygon of n sides where n>= 3 then its each exterior angle
Illustration: Find the sum of exterior angles of a 15 sided polygon.
Solution:The sum of exterior angle of a polygon is independent of the number of sides
Hence the sum of exterior angles of a 15 sided polygon is 3600.
Illustration: How many sides does a regular polygon has if its each exterior angle is a measure of 240?
Solution:Let us suppose the polygon has n sides
The exteriors angles of a pentagon are (m + 5)°, (2 m + 3)°, (3 m + 2)°, (4 m + 1)° and (5 m + 4)° respectively. Find the measure of each angle. | |||
| Right Option : B | |||
| View Explanation | |||
Find the number of sides in a regular polygon when the measure of each exterior angle is 60°. | |||
| Right Option : B | |||
| View Explanation | |||
The following figure shows a polygon with all its exterior angles. | |||
| Right Option : B | |||
| View Explanation | |||
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