# octagon?

#### yorkmanz

octagon?

1.What is the sum of the measures of the interior angles of a heptagon?

A. 1260∘
B. 2520∘
C. 900∘
D. 1800∘

5.If the sum of the interior angle measures of a polygon is 3600∘, how many sides does the polygon have?
A. 22 sides
B. 20 sides
C. 18 sides
D. 10 sides

3.What is the angle measure of each exterior angle of a regular octagon?
A. 45∘
B. 135∘
C. 360∘
D. 1080∘

#### topsquark

Forum Staff
How did you get your answer for 1? The rest are similar. Without knowing what you did we can't help you as well.

-Dan

#### HallsofIvy

MHF Helper
This is very strange. You title this "octagon" and the first word is "octagon" buy you ask about a "heptagon"?

In any case, imagine drawing lines from some point in the middle of the polygon to each vertex. For a polygon with n sides that creates n triangles. Since the angles in a triangle total 180 degrees ($$\displaystyle \pi$$ radians) the n triangles have total angles of 180 n degrees ($$\displaystyle n\pi$$ radians. However the angles at the central point total 360 degrees $$\displaystyle (\(\displaystyle 2\pi$$ radians) so the measures of the angles of the polygon itself total 180n- 360 degrees ($$\displaystyle n\pi- 2\pi= (n- 2)\pi$$ radians). For example, when n= 3 that is of course 3(180)- 360= 180 degrees ($$\displaystyle (3- 2)\pi= \pi$$ radians) or when n= 4, that is 4(180)- 360= 360 degrees ($$\displaystyle (4- 2)\pi= 2\pi$$ radians).\)

1 person

#### DenisB

Find the formula using George Google...