SOLUTION: Hello, I have been working on these math problems for a very long times, and I cannot figure out how to do them. Please help me out: 19.) Find the measures of an interior an

Question 272915: Hello,
I have been working on these math problems for a very long times, and I cannot figure out how to do them. Please help me out:
19.) Find the measures of an interior angle and an exterior angle of the indicated regular polygon.
Polygon: regular heptagon
Then number 25 is:
Find the value of n for each regular n-gon described
N-gon: each interior angle of the regular n-gon has a measure of 165 degrees
Thank you so much!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
19.) Find the measures of an interior angle and an exterior angle of the indicated regular polygon.
Polygon: regular heptagon
A heptagon has 7 sides.
The sum of the exterior angles always totals 360 degs
Ext angles = 360/7 =~ 51.43 degrees.
------------------------------------
The interior angles are 180 - Ext angle = 180 - (360/7) = 900/7 degs
=~ 128.57 degs
----------------
Then number 25 is:
Find the value of n for each regular n-gon described
N-gon: each interior angle of the regular n-gon has a measure of 165 degrees
-----------
The easiest way to do these is to find the Exterior angle first, = 180-165
Ext = 15 degs
The sum of Ext angles = 360
n = 360/15 = 24 sides and angles.

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