Question

what is the degree of the exterior angle for a regular 30 - gon?
16°
10°
12°
5°
none of these answers are correct.
question 4
1 pts
give the name for a convex polygon in which each exterior angle measures 45°.
hexagon
decagon
octagon
undecagon
none of these answers are correct.

Explanation:

Step1: Recall the formula for the measure of an exterior angle of a regular polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\). For a regular \(n -\)gon, the measure of each exterior angle \(\theta=\frac{360^{\circ}}{n}\)

Step2: Calculate the exterior angle for a 30 - gon

Given \(n = 30\), then \(\theta=\frac{360^{\circ}}{30}=12^{\circ}\)

Step3: Calculate the number of sides for a polygon with exterior angle \(45^{\circ}\)

Using the formula \(\theta=\frac{360^{\circ}}{n}\), when \(\theta = 45^{\circ}\), we solve for \(n\). Rearranging the formula gives \(n=\frac{360^{\circ}}{\theta}\). Substituting \(\theta = 45^{\circ}\), we get \(n=\frac{360^{\circ}}{45^{\circ}} = 8\)

Answer:

For the first question: \(12^{\circ}\) (the third option).
For the second question: Octagon (the third option).