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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.

 Apr 1, 2024
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n + n + d + n + 2d  = 180

3n + 3d  =  180

n + d =  60

n = 60  - d

 

( n + 2d)  - n =  56

2d = 56

d = 28

 

n = 60 - 28 =  32°

 

cool cool cool

 Apr 2, 2024

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