Question

What is the measurement of each interior angle of a 5 sided regular polygon?

Answer 1

See below

Explanation:

Given: 5-sided regular polygon

Regular means all of the sides and angles are congruent.

The interior angles of regular polygons sum to `(n-2)*180` where `n` = the number of sides.

The total sum of the interior angles of a 5-sided (pentagon) is
`(5-2)*180 = 540^@`

Since there are 5 sides, there are also 5 angles.

Divide the total sum by `5: " "(540^@)/5= 108^@`

The central angles sum to `360^@`.

Each central angle = `(360^@)/5 = 72^@`