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.

blackpanther Jun 13, 2024

#1**+1 **

If a polygon has 3 sides, then it has to be a triangle.

We can solve this problem by setting some variables. Let's set the smallest angle degrees as n.

Now, since the angles from an arithmetic sequence, each angle is increasing an equal amount.

This means if the first and last angle are 56 degrees apart, then the middle angle is \(56/2=23\) degrees bigger than n.

Thus, we can write the equation \(n+(n+23)+(n+56)=180\)

Solving this equation, we get

\(3n+79=180\\ 3n=101\\ n=101/3\)

So our final answer is 101/3

This is not a whole number, but it does work.

Thanks! :)

NotThatSmart Jun 13, 2024