xxsheevxx said:
The measure of each interior angle of a regular polygon is three times the measure of each exterior angle. How many sides does the polygon have?
I'm not sure what I'm supposed to do. Do I have to set the interior and exterior angle equal to each other?
Please show me step by step.
Thanks for your help and time!
You are expected to KNOW a few things before attempting this problem:
1) In a REGULAR polygon, each interior angle has the same measure, and each exterior angle has the same measure.
2) In any convex polygon (which would include any regular polygon), an interior angle and an exterior angle at the same vertex form a pair of supplementary angles.
3) The sum of the exterior angles in ANY convex polygon is 360.
Ok...
Let x = measure of an interior angle of the regular polygon
Let y = measure of an exterior angle of the regular polygon.
The problem says: The measure of each interior angle of a regular polygon is three times the measure of each exterior angle
So, x = 3y
And, since an interior angle and an exterior angle at the same vertex are supplementary,
interior angle + exterior angle = 180
x + y = 180
Now, you have a system of two equations in two variables:
x = 3y
x + y = 180
Solve that system to find the values for x and y.
Now...when you know the measure of ONE exterior angle (that will be the value of y) and you realize that the sum of ALL of the exterior angles is 360, you can find out how many exterior angles there are (they're all equal, remember).
And the number of exterior angles (one at each vertex) is the same as the number of sides in the polygon.
