Question

applying the polygon exterior angle sum theorem
what is the value of x?
72
84
96
252

Explanation:

Step1: Recall the polygon exterior angle sum theorem

The sum of the exterior angles of any polygon is \(360^{\circ}\).

Step2: Set up the equation

We have the equation \((x + 12)+57+60+51+108=360\).
First, simplify the left - hand side: \(x+12 + 57+60+51+108=x+(12 + 57+60+51+108)\).
Calculate \(12 + 57+60+51+108=(12+57)+(60+51)+108=69+111+108=288\).
So the equation becomes \(x + 288=360\).

Step3: Solve for \(x\)

Subtract 288 from both sides of the equation: \(x=360 - 288\).

Answer:

\(x = 72\)