Question

1. the measure of one exterior angle of a regular polygon measures 10°. how many sides does this polygon have?

Explanation:

Step1: Recall the formula for the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is always \(360^\circ\). For a regular polygon, all exterior angles are equal.

Step2: Let \(n\) be the number of sides of the regular polygon

If each exterior angle measures \(10^\circ\), and the sum of exterior angles is \(360^\circ\), we can set up the equation: \(n\times10^\circ = 360^\circ\)

Step3: Solve for \(n\)

To find \(n\), we divide both sides of the equation by \(10^\circ\): \(n=\frac{360^\circ}{10^\circ}\)

Step4: Calculate the value of \(n\)

\(\frac{360}{10}=36\)

Answer:

The polygon has 36 sides.