Question

if five of the exterior angles of a convex hexagon measure 50°, 56°, 60 71°, and 71°, find the measure of the sixth exterior angle. degrees if four of the exterior angles of a convex pentagon measure 48°, find the measure of the fifth exterior angle. m∠5 = 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 given exterior angles for the hexagon

For the hexagon, the sum of the five given exterior angles is \(50 + 56+60 + 71+71=308^{\circ}\).
Let the sixth exterior angle be \(x\). Then \(308 + x=360\). Solving for \(x\), we get \(x = 360-308=52^{\circ}\).

Step3: Calculate for the pentagon

For the pentagon, the sum of four given exterior angles (each \(48^{\circ}\)) is \(4\times48 = 192^{\circ}\). Let the fifth exterior angle be \(y\). Then \(192 + y=360\). Solving for \(y\), we get \(y=360 - 192=168^{\circ}\).

Answer:

For the hexagon: \(52\) degrees.
For the pentagon: \(168\) degrees.