Question

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

Answer 1

For a polygon with n sides, the interior angles add up to:

(n - 2) x 180

an octagon has 8 sides:

(8 - 2) * 180 = 6 * 180 = 1080

from the question,1 side measures 2x while 7 sides measure x. this means

7x + 2x = 1080

9x = 1080

x = 1080/9

x = 120°

if x=120°

2x=2(120°)=240°

so, the seven smaller angles are 120°. while the one larger angle is 240°