Question

exterior angles. in each diagram the exterior angles are shown. find the value of x.

Explanation:

Step1: Recall exterior - angle sum property

The sum of exterior angles of any polygon is 360°.

Step2: Solve for left - hand problem

For the left - hand polygon, we have \(70 + 110+80 + x=360\). Simplifying the left - hand side gives \(260 + x = 360\). Subtracting 260 from both sides: \(x=360 - 260=100\).

Step3: Solve for right - hand problem

For the right - hand pentagon, since all exterior angles are \(x\) and there are 5 exterior angles, we have \(5x = 360\). Dividing both sides by 5 gives \(x=\frac{360}{5}=72\).

Answer:

Problem on Left: 100
Problem on Right: 72