Question

Each enterior angle of a regular polygon is 108degree. Find the measure of an interior angle of a polygon with double the number of sides as the first polygon

Answer 1

Answer:

5

Step-by-step explanation:

If n is the number of sides, each interior angle I can be calculated by the following formula:

I = 180(n - 2)/n

Substitute:

108 = 180(n - 2)/n

Multiply both sides by n:

108n = 180(n - 2)

Distribute:

108n = 180n - 360

Subtract 180n from both sides:

108n - 180n = -360

Combine like terms:

-72n = -360

Divide both sides by -72:

n = 5

Answer 2

Answer:

5

Step-by-step explanation:

Given that, one interior angle is 108 degrees.

Sum of interior angles of a regular polygon = (n − 2) × 180°

Interior angle of a regular polygon = [(n − 2) × 180°] / n

108° = [(n − 2) × 180°]/n

108n = 180n - 360

72n = 360  

n = 5