2. Find the measure of each exterior angle of a re
(i) 9 sides
15 sides
Answers
Answer:
1260degree and 2340degree
Step-by-step explanation:
hope it helps
Correct Question -
Find the measure of each exterior angle of a polygon with -
[ I ] 9 sides .
[ II ] 15 sides.
Solution -
Part 1 -
Here , in the first part,
Number Of Sides Of Polygon = 9
Sum Of All Interior Angle -
=> ( n - 2 ) × 180°
=> ( 9 - 2 ) × 180°
=> 7 × 180°
=> 1260°
Now, measure of Each Interior Angle -
=> ( 1260° ) / ( 9 )
=> 140°
Now we know that -
The interior and exterior angle of a polygon are supplementary .
Hence ,
Exterior Angle = 180° - Interior Angle
=> 180° - 140°
=> 40°
Hence the exterior angle is 40°
Part 2 -
Here , in the second part,
Number Of Sides Of Polygon = 15
Sum Of All Interior Angle -
=> ( n - 2 ) × 180°
=> ( 15 - 2 ) × 180°
=> 13 × 180°
=> 2340°
Now, measure of Each Interior Angle -
=> ( 2340° ) / ( 15 )
=> 156°
Now we know that -
The interior and exterior angle of a polygon are supplementary .
Hence ,
Exterior Angle = 180° - Interior Angle
=> 180° - 156°
=> 24°
Hence the exterior angle is 24°