The interior angle measures of a pentagon form an arithmetic progression. The difference between the largest and smallest angle measures is 44 degrees. Find the measure of the smallest angle, in degrees.

SparshGarg
May 16, 2018

#1**+1 **

If the difference in the largest and smallest angle is 44 degrees.....then the common difference between each successive angle measure is 11°

And the sum of the angle measures is 540°

Let n be the smallest angle....so we have

n + (n + 11) + (n + 22) + (n + 33) + (n + 44) = 540 simplify

5n + 110 = 540 subtract 110 from both sides

5n = 430 divide both sides by 5

n = 86° = the smallest angle

CPhill
May 16, 2018