Question

What is the sum of the angle measures of a 37-gon?

Answer 1

There is an equation to solve this. It looks like:

Sum of interior angles = (n - 2) * 180 degrees

where n is the number of sides of the n-gon. In this case, 37.

Answer 2

the sum of all angles is (2n-4)*90
here n=37

Answer 3

(2n-4)*90 =(2*37-4)*90=(74-4)*90=70*90=6300

Answer 4

Sum of Interior angles: (3n-6)*60

Answer 5

In all seriousness you should use Logic's simplified formula.

Answer 6

Is it a REGULAR 37-gon? Does it matter?

I like to remember that the sum of EXTERNAL angles is ALWAYS 360º.

\(360º / 37 = 9.\overline{729}º\) -- The measure of each External Angle.

Internal Angels and External Angles are Supplementary

\(180º - 9.\overline{729}º = 170.\overline{270}º\) -- The measure of each Internal Angle.

I don't actually recommend this method over the \((n-2)\cdot 180º\) formula for such a question as the sum of the internal angles, but it can be useful if you forget.

Answer 7

The sum of the interior angles of a convex n-gon is (n - 2) * 180

Notice that I assume we are dealing with a convex polygon, as a concave one will wield infinitely many possible solutions.

Since we have a 37-gon here, the sum of the interior angles will be:
(37 - 2) * 180
= 6300 degrees