The measure of one angle of an octagon is twice that of the other seven angles. What is the measure of each angle?

Question

Help would be greatly appreciated.

Answer 1

Images don't work in comments, so I am posting this even though it is not really an answer.

Using Clayton's answer, and because Valentine's Day is just a couple of weeks away, it seemed appropriate to post this image of the octagon:

$\hspace{3.5cm}$

Answer 2

Hint: An octagon has $1080^\circ$, and you have the equation $$2\theta+\theta+\cdots+\theta=9\theta=1080^\circ.$$

Answer 3

The sum of the interior angles of an octagon is $1080^\circ$.

There are eight interior angles, one twice the measures of all others:

$7 \theta + (2\theta) = 1080^\circ$

Now solve for $\theta$ (which is the measure of the 7 equal angles),

and then compute $2\theta$, the measure of the angle that is twice the size of the other 7 interior angles.