What is the measure on an interior angle of this polygon?

How many sides does this polygon have?

a) 160°

b) 18 sides

Step-by-step explanation:

Interior angle = 180 - exterior

= 180 - 20 = 160°

Each angle of a regular polygon:

[(n-2)×180]/n = 160

180n - 360 = 160n

20n = 360

n = 18

Alternate approach for no. of sides:

360/n = each exterior angle

360/n = 20

n = 360/20 = 18

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.