Q15 of 805 Page 17

For a regular polygon of n sides, we have:

i. Sum of all exterior angles = ...... .


ii. Sum of all interior angles = ...... .


i.


ii.


Exp:


(i) We will learn how to find the sum of the exterior angles of a polygon having n sides.


We know that,


Exterior angle + interior adjacent angle = 180°


So, if the polygon has n sides, then


Sum of all exterior angles + Sum of all interior angles = n × 180°


So, the sum of all exterior angles = n × 180° - Sum of all interior angles


Sum of all exterior angles = n × 180° - (n -2) × 180°


= n × 180° - n × 180° + 2 × 180°


= 180°n - 180°n + 360°


= 360°


Therefore, sum of all exterior angles of the polygon having n sides = 360°


Therefore, measure of each exterior angle of the regular polygon = 360°/n


(ii) Exterior angle + interior adjacent angle = 180°


So, if the polygon has n sides, then


Each exterior angle + Each interior angle = 180°


Therefore , Each interior angles = 180° - 360°/n


More from this chapter

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13

Each interior angle of a polygon is 135. How many sides does it have?

 14

For a convex polygon of n sides, we have:

i. Sum of all exterior angles = ...... .


ii. Sum of all interior angles = ...... .


iii. Number of diagonals = ...... .


 16

i. Each interior angles of a regular octagon is

ii. The sum of all interior angle of a regular hexagon is


iii. Each exterior angle of a regular polygon is 60°. This polygon is a ...... .


iv. Each interior angle of a regular polygon is 108°. This polygon is a ...... .


v. A pentagon has ...... diagonals.


 17

Write ‘T’ for true and ‘F’ for false of each of the following:

i. The diagonals of a parallelogram are equal.


ii. The diagonals of a rectangle are perpendicular to each other.


iii. The diagonals of a rhombus bisect each other at right angles.


iv. Every rhombus is a kite.