Question

the ratio between exterior angle and interior angle of a regular polygon is 1 :5 find the measure of each interior angle, find the measure of each exterior angle and the no. of sides of the polygon.

Answer 1

let the ratio be 1x and 5x
therefore 1x+5x=180
6x=180
x=30
the formula to find no of sides of polygon is 360÷each exterior angle i.e
360÷30=12
the no of sides is 12 its a 12 sided polygon
please make it the brainliest answer!!!

Answer 2

Answer:

The measure of each interior angle = 150

The measure of each exterior angle = 30

The no. of sides of the polygon = 12

Step-by-step explanation:

Given,

The ratio between the exterior angle and interior angle of a regular polygon is 1:5

To find,

1. The measure of each interior angle,
2. The measure of each exterior angle
3. The no. of sides of the polygon.

Recall the formula

Each exterior angle of a regular polygon = $\frac{360}{n}$ ---------------(1)

Each interior angle of a regular polygon = $\frac{180(n-2)}{n}$---------------(2)

where 'n' is the number of sides of the polygon.

Solution

Since The ratio between the exterior angle and interior angle of a regular polygon is 1:5 we have

$\frac{\frac{360}{n} }{\frac{180(n-2)}{n} }$ = $\frac{1}{5}$

$\frac{360}{180(n-2)}$ = $\frac{1}{5}$

$\frac{2}{n-2} = \frac{1}{5}$

n-2 = 10

n = 12

The number of sides of the polygon, n= 12

Substituting the value of 'n' in equation (2) we get

The measure of each interior angle = $\frac{180(12-2)}{12}$

= $\frac{180X10}{12}$

= 150

The measure of each interior angle = 150

Substituting the value of 'n' in equation (1) we get

The measure of each exterior angle = $\frac{360}{12}$

= 30

The measure of each exterior angle = 30

Hence we have,

The measure of each interior angle = 150

The measure of each exterior angle = 30

The no. of sides of the polygon = 12

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