Question

the number of sides of 2 regular polygon are 5:4 and the difference between their angles is 9.find number of sides of polygon

Answer 1

The number of sides will be 10, 8

hope it may help you

Answer 2

Given:

Ratio of  sides of two regular  polygon=5:4

Difference between their angles=9

To find:

Number of sides of polygon

Solution:

Let

Total number of sides of one regular polygon=5x

Total number of sides of other regular polygon=4x

We know that

Measure of each interior angle=$\frac{n-2}{n}\times 180$

Using the formula

Angle measure  of  one regular polygon with total number of sides 5x=$\frac{5x-2}{5x}\times 180$

Angle measure  of  other regular polygon with total number of sides 4x

=$\frac{4x-2}{4x}\times 180$

According to question

$\frac{5x-2}{5x}\times 180-\frac{4x-2}{4x}\times 180=9$

$180\frac{(20x-8-20x+10)}{20x}=9$

$\frac{18}{x}=9$

$x=\frac{18}{9}=2$

Number of sides of one polygon=2(5)=10

Number of sides of other polygon=2(4)=8