Answer: measure of larger angle = 240 degrees measure of each of the smaller angles = 120 degrees
Explanation: 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 = 1080°
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
