If the measure of each angle of a regular polygon is 174 degrees, then the measure of each exterior angle is??

Explanation:

This is because any pair of adjacent interior and exterior angles must add to 180 degrees. The two angles are supplementary. They form a straight line when glued together.

If x is the exterior angle, then x+174 = 180 solves to x = 6 after subtracting 174 from both sides.

Side note: This regular polygon has 360/x = 360/6 = 60 sides.

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value