Question

One of the interior angles of a regular polygon is 144. fine the number of sides of the polygon ​

Answer 1

10

Explanation:

In any polygon

exterior angle + interior angle = 180° , thus

exterior angle + 144 = 180 ( subtract 144 from both sides )

exterior angle = 36°

The sum of the exterior angles = 360°

Thus number of sides n is calculated as

n = 360 ÷ 36 = 10

Answer 2

The polygon has 10 sides

Explanation:

One of the interior angles of a polygon can be found using the formula

`((n - 2) *180\degree )/(n)`

where n is the number of sides of the polygon

From the question

One of the interior angles = 144

To find the number of sides substitute this value into the above formula and solve for n

That's

`144 = ((n - 2) * 180)/(n)`

Cross multiply

We have

`144n = (n - 2) * 180`

Expand the terms in the bracket

`144n = 180n - 360`

Group like terms

`144n - 180n = - 360 \\ \\ - 36n = - 360`

Divide both sides by - 36

That's

`( - 36n)/( - 36) = ( - 360)/( - 36)`

We have the final answer as

n = 10 sides

Hope this helps you