Question

if five of the exterior angles of a convex hexagon measure 50°, 59°, 55° 71°, and 79°, find the measure of the sixth exterior angle.
______ degrees

question 14
1 pts

if four of the exterior angles of a convex pentagon measure 67°, 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

Sum of given angles \(=50 + 59+55 + 71+79\)
\(=50+59 = 109\), \(109+55=164\), \(164 + 71=235\), \(235+79 = 314\)

Step3: Find the sixth exterior angle of the hexagon

Let the sixth angle be \(x\). Then \(x=360-(50 + 59+55 + 71+79)\)
\(x = 360-314=46\)

Step4: Calculate for the pentagon

Sum of given angles (pentagon, 4 angles each \(67^{\circ}\)) \(=4\times67=268\)
Let the fifth angle be \(y\). Then \(y = 360-4\times67\)
\(y=360 - 268=92\)

Answer:

For the hexagon: \(46\) degrees
For the pentagon: \(92\) degrees