octagon?

Jan 2019
18
0
toronto
octagon?

PLEASE HELP


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

A. 1260∘
B. 2520∘
C. 900∘
D. 1800∘

my answer is C

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

MY ANSWER ?

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

MY ANSWER ?
 

topsquark

Forum Staff
Jan 2006
11,565
3,452
Wellsville, NY
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
Apr 2005
20,249
7,909
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).\)
 
  • Like
Reactions: 1 person
Feb 2015
2,255
510
Ottawa Ontario
Find the formula using George Google...