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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.

 Dec 24, 2023
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Let the three angles be a, a+d, and a+2d, where d is the common difference. Then a+2d−a=56∘, so d=28∘.

 

The sum of the angles in a triangle is 180∘, so a+(a+d)+(a+2d)=180∘

 

Substituting d=28∘, we get 3a+84∘=180∘, so a=32∘. Thus, the smallest angle is 32∘​.

 Dec 24, 2023

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