Question

The measure of an interior angle of a regular polygon is 170°. How many sides make up the regular polygon?

Answer 1

\[\left( n-2 \right)*180/n\] gives you the size of the interior angle of any regular polygon with side n. this means that:
\[\left( n-2 \right)*180/n\] = 170
solve for n
\[\left( n-2)*180 \right) = 170n\]
180n -360 = 170n
10n =360
n = 36

Answer 2

Interior 170 -> exterior = 10
360/10 = 36