Question

All the angles of a 9 sided polygon are equal.
(a) Calculate one outer angle.
(b) Calculate one inner angle.
(c) Write the sum of all inner angles.​

Answer 1

Answer:

a) 40°

b)140°

c) 1260°

Step-by-step explanation:

each interior angle = n-2 * 180/n= 9-2*180/9 =7*20=140

each exterior angle = 180- 140 (linear pair) = 40

sum of interior angle = n-2 *180=9-2*180 =7*180= 1260°

Answer 2

Given:

All the angles of a 9 sided polygon are equal

To find:

(a) Calculate one outer angle

(b) Calculate one inner angle

(c) Write the sum of all inner angles

Solution:

The outer angle is 40°, the inner angle is 140°, and the sum of all inner angles is 1,260°.

We can find the angles by following the given steps-

We know that polygon has 9 sides and all its angles are equal.

The sides of the polygon, n=9

(a) We know that the outer angle of any polygon can be obtained by dividing 360° by the number of sides.

So, the outer angle=360°/number of sides of the polygon

=360°/9

=40°

(b) Since the inner and the outer angle of a polygon form a linear pair, their sum is 180°.

The inner angle of the polygon+Outer angle of the polygon=180°

On putting the value of the outer angle, we get

The inner angle of the polygon+40°=180°

The inner angle of the polygon=180°-40°

=140°

(c) In any polygon, the sum of all its inner angles is calculated by multiplying the number of sides minus two with 180°.

So, the sum of all inner angles of the polygon=(Number of sides-2)×180°

=(n-2)×180°

=(9-2)×180°

=7×180°

=1,260°

Therefore, the outer angle is 40°, the inner angle is 140°, and the sum of all inner angles is 1,260°.