Question

What is the number of sides of a regular polygon if the angle subtended by all the sides is 72?

Answer 1

Hello there!

We have to use this formula:

   Sum of all angles $=180\left(n-2\right)$, where $n$ = number of sides.

In a regular polygon of $n$ sides, we know that each angle is equal. So, when we divide the total sum by the number of sides, we get the measure of one angle, which is shown below:

$sum=180\left(n-2\right)$

One interior angle$=\dfrac{180\left(n-2\right)}{n}$

It is given that the interior angle of that regular polygon is 72°. We can substitute this value into the formula as follows:

One interior angle$=\dfrac{180\left(n-2\right)}{n}$

$72=\dfrac{180\left(n-2\right)}{n}$

$72 \times n=180\left(n-2\right)$

$72n=180\left(n-2\right)$

$72n=180n-360$

$72n-180n=-360$

$-36n=-360$

$n=\dfrac{-360}{-36}$

$n=10$

Therefore, the polygon has 10 sides.

Please mark this as Brainliest if you found this helpful!