Question

What is the sum of the measures of the interior angles of an 11-gon?



A.
2340°


B.
1620°


C.
1800°


D.
1980°

Answer 1

#1 rule to stick in your head... The sum of the EXTERIOR angles of a polygon sum to 360º. EVERY TIME.

Does that help?

Answer 2

Not really.

Answer 3

Draw it out if you're stuck...then fool around with what tkhunny said...

Answer 4

I already tried that and it didn't work, and what am I supposed to do with the exterior?

Answer 5

It worked. You just didn't see it. Hints...

We are assuming this is a REGULAR 11-gon.

How many exterior angles are there for an 11-gon.
What is the measure of each of the exterior angles?
What is the relationship between Exterior and Interior angles?

Answer 6

11, 32.72, and they are both part of the same angle?

Answer 7

Glad you came back. Connection problems.

360 / 11 = 32.72727 -- Good

Not just "part or the same", but they are Supplementary. Thus, they add to 180º.

The Interior angles measure what, then?

Answer 8

When they are all added up then they equal 360*.

Answer 9

When you add up the EXTERIOR angles, you get 360º.
When you add up the supplementary INTERIOR angles, you get...?

Answer 10

The sum of the measures of the interior angles of a convex n-gon is \[\left( n - 2\right)\times180º\]
Replace n with 11.