SOLUTION: An Exterior Angle Of A Regular Polygon Is Four Times Smaller Than Its Interior Angle.how Many Sides Does The Polygon Have?

Question 626636: An Exterior Angle Of A Regular Polygon Is Four Times Smaller Than Its Interior Angle.how Many Sides Does The Polygon Have?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An Exterior Angle Of A Regular Polygon Is Four Times Smaller Than Its Interior Angle.how Many Sides Does The Polygon Have?
====
Let the interior angle be "4x".
Then the exterior angle will be "x".
---
Equation: x + 4x = 180
5x = 180
x = 36 degrees (measure of each exterior angle)
---
The sum of all of the exterior angles is always 360 degrees.
---
# of sides = # of exterior angles = 360/36 = 10
======================
Cheers,
Stan H.
RELATED QUESTIONS
The measure of each interior angle of a regular polygon is 14 times the measure of an... (answered by solver91311)

The measure of each interior angle of a regular polygon is 14 times the measure of an... (answered by stanbon)

the measure of each interior angle of a regular polygon is 14 times the measure of an... (answered by stanbon)

The measure of each interior angle of a regular polygon is fourteen times that of an... (answered by Alan3354)

The measure of each interior angle of a regular polygon is eight times that of an... (answered by Alan3354)

The measure of each interior angle of a regular polygon is 3 times larger than each... (answered by Alan3354)

Each exterior angle of a regular polygon measure 15 degrees how many sides does it... (answered by Alan3354)

The measure of one interior angle of a regular polygon is two times the measure of one of (answered by stanbon)

The exterior angle of a regular polygon is one-third of its interior angle. How many... (answered by josgarithmetic,MathTherapy)