Question

if five of the exterior angles of a convex hexagon measure 74°, 71°, 53°, 58°, 60°, find the measure of the sixth exterior angle.
____ 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: Set up an equation

Let the measure of the sixth exterior angle be \(x\). We know that the sum of the five given exterior angles \((74^{\circ}+71^{\circ}+53^{\circ}+58^{\circ}+60^{\circ})\) plus \(x\) equals \(360^{\circ}\).
First, calculate the sum of the five given angles: \(74 + 71+53+58+60=(74 + 71)+(53+58)+60 = 145+111 + 60=316^{\circ}\).
Then, using the equation \(316^{\circ}+x = 360^{\circ}\).

Step3: Solve for \(x\)

Subtract \(316^{\circ}\) from both sides of the equation: \(x=360^{\circ}-316^{\circ}\).

Answer:

\(44\)