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

Guest Oct 21, 2017

#1**+1 **

Call the smallest angle measure, N

And the largest N + 44

And the sum of the interior angle measures of a pentagon = 540°

So

N + (N + d) + (N + 2d) + (N + 3d) + (N + 4d) = 540

Where d is the common difference....simplifying, we have that

5N + 10d = 540 (1) and

N + 44 = N + 4d → 44 = 4d → 11 = d sub this into (1)

5N + 10 (11) = 540

5N + 110 = 540

5N = 430 divide through by 5

N = 86°

CPhill
Oct 21, 2017