octagon?

[yorkmanz]

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 ?

 

[pka]

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 ?

Have a look HERE

 

[Harry_the_cat]

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 ?

I'm not giving you the answers, but a lesson!
1. Draw a triangle (3 sides). What is the sum of the interior angles?
2. Draw a square (or any quadrilateral for that matter) (4 sides). What is the sum of the interior angles?
3. Lets skip one and draw a regular hexagon (6 sides). Draw in the diagonals. Each triangle is equilateral. So each interior angle is 120 degrees. Can you see that? So, what is the sum of the interior angles?
Now summarise your findings:

3 sides leads to an interior angle sum of ________. How many lots of 180 degrees is that?
4 sides leads to an interior angle sum of ________. How many lots of 180 degrees is that?

6 sides leads to an interior angle sum of ________. How many lots of 180 degrees is that?

So,
n sides leads to an interior angle sum of __________ lots of 180 degrees.
​

Now you have a rule to help you solve your problems.

BTW Your answer to Q1 is correct, so maybe you know the rule. You need to use it as your first step in Q2 and Q3.

 

[HallsofIvy]

Given a polygon with n sides, take any point in the interior of the polygon and draw the n lines from that point to the n vertices. That divides the polygon into n triangles, each with interior angle sum 180 degrees. The total of all those angles is 180 degrees. But that includes the angles at the interior point. Those angles, forming a complete circle around the interior point, sum to 360 degrees. We need to subtract that off. The total degree measure of the interior angles of a polygon with n sides is 180n- 360= 180(n- 2). As a check, if the polygon is a triangle, so n= 3, that is 180(3-2)= 180. If the polygon is a rectangle, so n= 4, that is 180(4- 2)= 360, exactly what we would get by multiplying the 90 degree angles by 4.

1) A heptagon has 7 sides. The sum of interior angles is 180(7- 2)= 180(5)= 900 degrees.

2) A polygon has interior angle sum 3600 degrees. 180(n- 2)= 3600 so n- 2= 3600/180= 20. The polygon has 22 sides.


3. The "exterior angles" of a polygon are the angles between one side of the polygon and the adjacent side extended. An interior angle and the exterior angle at the same vertex are complementary. The interior angles in an octagon (8 sides) sum to 180(8- 2)= 1080 so each angle in a regular octagon is 1080/8= 135 degrees. Each exterior angle is 180- 135= 45 degrees.