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.

kittykat Dec 24, 2023

#1**0 **

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∘.

BuiIderBoi Dec 24, 2023