Calculate the measure of each angle of an octagon, where the measures of an angle form an arithmetic sequence and the least measure is 58 degrees.

Question

Calculate the measure of each angle of an octagon, where the measures of an angle form an arithmetic  sequence and the least measure is 58 degrees.

campbell_st · Answer

the angle sum of a ploygon is (n - 2)*180 = 1080

if its a arithmetic sequence you know the 1st term a = 58, n = 8 you need to find the common difference

Use the sum of an arithmetic sequence to find the common difference

$$1080 = \frac{8}{2}[2\times58 + ( 8 - 1)d]$$

solve for d

$$\frac{2160}{8} = 116 + 7d$$

$$270 = 116 + 7d$$

d = 22

the common difference is 22 degrees then the angles are

58, 80, 102, 124, 146, 168, 190, 212