Answer:
Part a) The measure of an exterior angle is 60°
Part b) The measure of an interior angle is 120°
Step-by-step explanation:
step 1
Find the value of x
we know that
A regular polygon has equal sides and equal interior angles
The sum of an interior angle plus an exterior angle must be equal to 180 degrees (supplementary angles)
so
[tex]2x+4x=180[/tex]
solve for x
[tex]6x=180[/tex]
[tex]x=30[/tex]
step 2
Find the measure of an exterior angle
2x
substitute the value of x
[tex]2x=2(30)=60\°[/tex]
step 3
Find the measure of an interior angle
4x
substitute the value of x
[tex]4x=4(30)=120\°[/tex]
In this problem the regular polygon is a hexagon
