Quadrilaterals and Polygons: Polygons

Think & Click: Exterior Angles in a Polygon

Now, you try. Complete the Think & Click activity by looking at the problem below, thinking about it, and then clicking on the question to reveal the solution.

Find the measure of each exterior angle in a regular 20-gon.

Solution: $the fraction 360 degrees over 20 equals 18 degrees$

Find the measure of each exterior angle in a regular octagon.

$the fraction 360 degrees over 8 equals 45 degrees$

Find the value of x in the figure below.

five-sided figure with exterior angles 45x minus 13 degrees, 15x plus 7 degrees, 13x plus 9 degrees, 50x minus 43 degrees and 10x plus 1 degrees

Solution
(15x + 7) + (13x + 9) + (50x – 43) + (10x + 1) + (45x – 13) = 360
133x – 39 = 360
133x = 399
x = 3

Find the measure of angle EBC

three-sided figure with exterior angles 7x minus 40 degrees, 4x plus 4 degrees and 5x minus 4 degrees

Solution
(4x + 4) + (5x – 4) + (7x – 40) = 360
16x – 40 = 360
16x = 400
x = 25
angle EBC = 5(25) – 4 = 121°