Question

The measure of an interior angle of a regular polygon is four times the measure of an exterior angle of the same polygon. What is the name of the polygon?

Answer 1

The name of polygon is decagon

Solution:

Given that measure of an interior angle of a regular polygon is four times the measure of an exterior angle of the same polygon

To find the name of polygon

Let us first find the number of sides of polygon

The interior angle of a regular polygon can be determined with the following formula:

`(180(n-2))/(n)`

where n represents the number of sides the polygon has

The measure of each exterior angle of a regular polygon can be determined using the following formula:

`(360)/(n)`

where n represents the number of sides the polygon has

From given statement,

measure of an interior angle = 4 times the measure of exterior angle

`(180(n-2))/(n) = 4 * (360)/(n)\\\\180(n-2) = 4 * 360\\\\180n - 360 = 1440\\\\180n = 1440 + 360\\\\180n = 1800\\\\n = 10`

Thus number of sides of polygon is 10

A decagon is a 10-sided polygon

Number of sides = 10 (it is a decagon)

Thus the name of polygon is decagon