Question

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

Answer 1

Answer:

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

Answer 2

Answer:

The polygon has 10 sides

Step-by-step explanation:

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

$\frac{(n - 2) \times180\degree }{n}$

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

$144 = \frac{(n - 2) \times 180}{n}$

Cross multiply

We have

$144n = (n - 2) \times 180$

Expand the terms in the bracket

$144n = 180n - 360$

Group like terms

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

Divide both sides by - 36

That's

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

We have the final answer as

n = 10 sides

Hope this helps you