Question

The sum of angles of a polygon is1800°.

a) What is the sum of the angles of a polygon with one side more ?

b) What is the sum of the angles a polygon with one side less​

Answer 1

One Side angle will be 900

Answer 2

Given:

The sum of angles of the polygon = 1800°

To find:

a) What is the sum of the angles of a polygon with one side more ?

b) What is the sum of the angles a polygon with one side less​?

Solution:

Sum of all the angle in a polygon with n sides = n*180°

If the sum of angle all the sides is 1800°, then:

n* 180° = 1800°

n = 1800°/ 180° = 10

• When the polygon has one more side then n' = n+1

Then sum of angles = (n+ 1)*180°

Where n = 10

Then sum of angles = (10 + 1)* 180°

= 11 * 180° = 1620°

Therefore the sum of angles is 1980°.

• When the polygon has one side less then n'' = n-1

Then sum of angles = (n-1)*180°

Where n = 10

Then sum of angles = (10 - 1)* 180°

= 9 * 180° = 1620°

Therefore the sum of angles is 1620°.