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

Measure of 7 angles is 144 degrees each and measure of 8th angle is 72 degrees.

Explanation:

An octagon is an 8-sided polygon. We are given that 7 angles of the octagon have the same measure while one angle is 1/2 times (i.e. half of the other angles). So if each of the 7 angles measure x degrees, the measure of 8th angles would be x/2 degrees.

The sum of internal angles of a polygon can be calculated as:

180(n-2), where n is the number of sides of the polygon. So for an octagon n=8, therefore the sum of internal angles of octagon would be:

180(8-2)= 180 x 6 = 1080 degrees.

We can write the equation as:

Sum of internal angles of octagon = 1080

`7x + (x)/(2)  = 1080\\\\(15x)/(2)=1080\\\\15x=2160\\\\ x=144`

This means, 7 of the angles measure 144 degrees and one angle measures 144/2 = 72 degrees.