+712 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 $3$ sides, then find the smallest angle, in degrees.
+1077
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 $3$ sides, then find the smallest angle, in degrees.
Call the three angles a, b, and c, in order of size.
The problem states c – a = 56 ==>> c = a + 56
The angles are in an arithmetic
sequence, so b – a = (1/2)(56) ==>> b = a + 28
The sum of the three angles of a
triangle is 180, so a + b + c = 180 ==>> (a) + (a + 28) + (a + 56) = 180
3a + 84 = 180
3a = 96
a = 32
check answer
a + b + c = 180
32 + (32 + 28) + (32 + 56) = 180
180 = 180 ==>> True
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