# The Number of Sides of Two Regular Polygons Are as 5 : 4 and the Difference Between Their Angles is 9°. Find the Number of Sides of the Polygons. - Mathematics

The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.

#### Solution

Let the number of sides in the first polygon be 5x and the number of sides in the second polygon be 4x.
We know:
Angle of an n-sided regular polygon = $\left( \frac{n - 2}{n} \right)180^\circ$
Thus, we have:
Angle of the first polygon = $\left( \frac{5x - 2}{5x} \right)180^\circ$
Angle of the second polygon = $\left( \frac{4x - 2}{4x} \right)180^\circ$
Now,
$\left( \frac{5x - 2}{5x} \right)180 - \left( \frac{4x - 2}{4x} \right)180 = 9$
$\Rightarrow 180\left( \frac{4(5x - 2) - 5(4x - 2)}{20x} \right) = 9$
$\Rightarrow \frac{20x - 8 - 20x + 10}{20x} = \frac{9}{180}$
$\Rightarrow \frac{2}{20x} = \frac{1}{20}$
$\Rightarrow \frac{2}{x} = 1$
$\Rightarrow x = 2$
Thus, we have:
Number of sides in the first polygon = 5x = 10
Number of sides in the second polygon = 4x = 8

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 4 Measurement of Angles
Exercise 4.1 | Q 10 | Page 15