Question

4. Complete this statement: The sum of the measures of the exterior angles of an n-gon one at each vertex, is ____ degrees. (1 point)
360
(n-2) 180
(n-2) 180/n
180n

Answer 1

Consider an octagon first.

Answer 2

This inner angle is just \(360^\circ /8\)

Answer 3

The outer angles must add to it to be \(180^\circ\) since it is a triangle.
Thus the sum of the outer angles is \(180^\circ - 360^\circ / 8\)

Answer 4

There are \(8\) of them, so the sum of exterior angles will be \[
8\times \left(180^\circ - \frac{360^\circ }{8}\right)
\]

Answer 5

Change \(8\) to \(n\): \[
n\left(180^\circ - \frac{360^\circ }{n}\right) = 180^\circ n-360^\circ = 180^\circ n-180^\circ (2) = 180^\circ (n-2)
\]

Answer 6

So the sum of the exterior angles is \(180^\circ (n-2)\) and each exterior angle is \(180^\circ (n-2)/n\)

Answer 7

so its c?

Answer 8

What is the question asking for?

Answer 9

its asking for the degrees of the vertex at each angle

Answer 10

@baddiemaddie >>>> so its c? No.

The sum of the measures of the exterior angles of an n-gon one at each vertex, is ____ degrees.

Polygon Exterior Angle Sum Theorem

Read the first sentence here:

http://hotmath.com/hotmath_help/topics/polygon-exterior-angle-sum-theorem.html

Answer 11

@baddiemaddie Do you see the answer?

Answer 12

Yes thanks!

Answer 13

That's good news.