+1911 The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $4$ sides, then find the smallest angle, in degrees.
+129852 Let d be the common difference between the angle measures
Let a be the smallest angle and a + 56 = the largest = a + 3d
The sum of the interior angles = 360
So
a + 3d = a + 56
3d = 56
d = 56/3
So
( a ) + (a + 56/3) + (a + 2*56/3) + (a + 3*56/3) = 360
4a + (6)(56/3) = 360
4a + 112 = 360
4a = 360 - 112
4a = 248
a = 248 / 4 = 62 (degrees)
