Math
posted by Brianna
1. The measure of an interior angle of a regular polygon is 20 more than thrice the measure of its adjacent exterior angle. Find the number of sides of the polygon and its total number of diagonals.
2. Find the sum and difference between the sum of the measures of the interior angles of a convex 23gon and 14gon.

Reiny
1. let the number of sides be n
each interior angle = 180(n2)/n
exterior angle = 360/n
180(n2)/n = 3(360/n) + 20
times n
180(n2) = 1080 + 20n
180n  360 = 1080 + 20n
160n = 1440
n = 9
We have a 9gon, which is called a enneagon or nonagon
check:
interior angle = 180(7)/9 = 140
exterior angle = 360/9 = 40
is 3 times 40 + 20 = 140 ? , YES
2.
sum interior angles of 23gon= 180(21) = 3780
sum of interior angles of 14gon = ....
then take their sum and difference
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