The interior angle measures of a pentagon form an arithmetic progression. The difference between the largest and smallest angle measures is 48 degrees. Find the measure of the smallest angle, in degrees.
+128475 Call the common difference between the angles, D
And call the measure of the smallest angle, A
And we know that the sum of the interior angles = (5-2) (180) = 3 *180 = 540°
So we have that
A + (A + D ) + (A + 2D) + (A + 3D) + (A + 4D) = 540
5A + 10D = 540 (1)
And we know that (A + 4D) - A = 48
So, simplifying.......4D = 48
D = 12 (2)
Sub (2) into (1) and we have that
5A + 10(12) = 540
5A + 120 = 540
5A = 540 -120
5A = 420
A = 420/5 = 84°
