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

10

Step-by-step 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

Step-by-step explanation:

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

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

Cross multiply

We have

Expand the terms in the bracket

Group like terms

Divide both sides by - 36

That's

We have the final answer as

Hope this helps you