Question

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?

Answer 1

let x be the exterior angle, and 3x be the interior angle. the two must add to 180 since they are a linear pair. so 3x + x = 180, x = 45, 3x=135. the sum of the measures of a regular polygon of n sides is: 180*(n-2). divide by n to get the average measure, and set equal to 135 (since your interior angles are 135 degrees)

\[135 = \frac{180*(n-2)}{n}\]

solve for n

Answer 2

i didn't know this formula from memory; had to look it up; you probably will have to do the same for similar problems

Answer 3

8 sides

Answer 4

thanks, and yeah ik the formula.

Answer 5

that's right good job

Answer 6

thanks for helping. :)

Answer 7

anytime :)