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.
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