# octagon?

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### 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∘

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### Re: octagon?

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

A. 1260∘
B. 2520∘
C. 900∘
D. 1800∘

Imagine a polygon with n sides. Draw lines from a point in the center of the polygon to each vertex. That divides the polygon into n triangles each with angle sum 180 degrees so a total of 180n degrees. But that counts the angles at the center point also. Since the lines go all the way around the polygon those angles total 360 degrees. So the interior angles must sum to 180n- 360= 180n- 180(2)= 180(n- 2).A "heptagon" has 7 sides so the interior angles total 180(7- 2)= 180(5)= 900 degrees. C is correct.

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

As above, if a polygon has n sides the interior angles total 180(n- 2) degrees. Solve 180(n- 2)= 3600.

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

An "exterior angle" in a polygon is the angle between one side and and the extension of the next side. Imagine walking around a polygon. You walk in a straight line until you reach a vertex then you make a turn equal to the exterior angle there. When you have reached your beginning point again, you are facing in the same direction you were initially- you have turned a total of 360 degrees. In a regular polygon all those angles are the same so each is 360 divided by the number of vertices. An octagon has 8 vertices.

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