Question

if four of the exterior angles of a convex pentagon measure 49°, find the measure of the fifth exterior angle. 160° 176° 164° 187° none of these answers are correct. question 6 1 pts what is the sum of the exterior angles of a 21 - gon? sum = ______ 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 sum of the four given exterior angles

The four given exterior angles each measure \(49^{\circ}\), so their sum is \(4\times49^{\circ}=196^{\circ}\).

Step3: Find the measure of the fifth exterior angle

Let the fifth exterior angle be \(x\). Using the formula for the sum of exterior angles (\(360^{\circ}\)), we have \(x + 196^{\circ}=360^{\circ}\). Solving for \(x\), we get \(x=360^{\circ}-196^{\circ}=164^{\circ}\).

Step1: Recall the sum of exterior angles of a polygon

The sum of the exterior angles of any convex polygon is a constant value. It does not depend on the number of sides \(n\) of the polygon.

Answer:

\(164^{\circ}\)

For the second question: