Question

if four of the exterior angles of a convex pentagon measure 52°, find the measure of the fifth exterior angle.
m∠5 =
________ degrees

question 8
1 pts

what is the degree of the exterior angle for a regular pentagon?

________ degrees

Explanation:

Step1: Recall the sum of exterior angles of a polygon

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

Step2: Calculate the measure of the fifth exterior angle

Let the measure of the fifth exterior angle be \(x\).
We know that \(4\times52^{\circ}+x = 360^{\circ}\).
First, calculate \(4\times52^{\circ}=208^{\circ}\).
Then, \(x=360^{\circ}-208^{\circ}\).
\(x = 152^{\circ}\)

Step3: For a regular pentagon

The formula for the measure of each exterior angle of a regular polygon is \(\frac{360^{\circ}}{n}\), where \(n\) is the number of sides.
For a pentagon, \(n = 5\).
So, the measure of each exterior angle is \(\frac{360^{\circ}}{5}=72^{\circ}\)

Answer:

For the first question: \(152\)
For the second question: \(72\)