+0

# Geometry

0
1
1
+455

In a certain regular polygon, the measure of each interior angle is \$2\$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

Jun 3, 2024

#1
+806
+1

We can write an equation.

The measure of an interior angle is \( (n - 2)(180^\circ) / n \) where n is the sidelengths. Since, the exterior angle is 180  minues the interior angle, we have

\( (n - 2)(180) / n = 2 · ( 180 - (n - 2)(180) / n ) \\ (n - 2)(180) / n = 360 - 2 · (n - 2)(180) / n ) \\ 3 · (n - 2)(180) / n ) = 360 \\(n-2)(180)/n=120 \\(n-2)/n=2/3 \\n-2=2n/3 \\3n-6=2n \\n=6\)

We can check our work.

A 6-sided polygon has an interior of 120 and exterior of 60.

Thank! :)

Jun 3, 2024

#1
+806
+1

We can write an equation.

The measure of an interior angle is \( (n - 2)(180^\circ) / n \) where n is the sidelengths. Since, the exterior angle is 180  minues the interior angle, we have

\( (n - 2)(180) / n = 2 · ( 180 - (n - 2)(180) / n ) \\ (n - 2)(180) / n = 360 - 2 · (n - 2)(180) / n ) \\ 3 · (n - 2)(180) / n ) = 360 \\(n-2)(180)/n=120 \\(n-2)/n=2/3 \\n-2=2n/3 \\3n-6=2n \\n=6\)

We can check our work.

A 6-sided polygon has an interior of 120 and exterior of 60.

Thank! :)

NotThatSmart Jun 3, 2024