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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.

 Mar 12, 2024
 #1
avatar+128406 
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Call the smallest angle x and the common difference d

x + (x + d) + (x + 2d)  =  180

3x + 3d   = 180

x + d   = 60

 

(x + 2d) - x  = 56

2d = 56

d = 56 / 2 = 28

 

x + 28  =  60

x = 60  -  28  =    32°  =  the smallest angle

 

cool cool cool

 Mar 12, 2024

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