He measure of one angle of an octagon is twice that of the other seven angles. what is the measure of each angle? answer: ,

Accepted Solution

measure of larger angle = 240 degrees
measure of each of the smaller angles = 120 degrees

In any polygon, the sum of measures of interior angles can be calculated using the following rule:
sum of interior angles = (n-2)*180 where n is the number of sides

Now, for an octagon, n=8, this means that:
sum of measures of interior angles = (8-2)*180 = 1080Β°

An octagon has 8 interior angles, one of which is twice the measure of the others.
Assume that each of the 7 smaller angles is x degrees and that the larger angle is 2x degrees

Computing their summation, we will find that:
x + x + x + x + x + x + x + 2x = 1080
9x = 1080
x = 120

This means that:
each one of the smaller angles = x = 120 degrees
the larger angle = 2x = 2 * 120 = 240 degrees

Hope this helps :)