Question

the polygon exterior angle sum theorem
what is the value of x?

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 exterior angles \(92^{\circ},43^{\circ},61^{\circ},56^{\circ},80^{\circ},(2x)^{\circ}\). So, \(92 + 43+61 + 56+80+2x=360\).

Step3: Simplify the left - hand side of the equation

First, add the known angles: \(92 + 43+61 + 56+80=(92 + 43)+(61 + 56)+80 = 135+117+80=332\). The equation becomes \(332 + 2x=360\).

Step4: Solve for \(x\)

Subtract \(332\) from both sides: \(2x=360 - 332\), so \(2x = 28\). Then divide both sides by \(2\): \(x=\frac{28}{2}=14\).

Answer:

\(x = 14\)