A hexagon has two exterior angles that measure (3x), two exterior angles that measure(2x+20), and two exterior angle that measures(x+34). If all of these angles have different vertices, what is the measure of the smallest exterior angle?
Sum of exterior angles of any polygon is 360°
In this case:
2 ∙ 3 x + 2 ( 2 x + 20° ) + 2 ( x + 34° ) = 360°
6 x + 4 x + 40° + 2 x + 68° = 360°
12 x + 108° = 360°
Subtract 108° to both sides
12 x = 252°
x = 252° / 12
x = 21°
The angles are:
3 x = 3 ∙ 21° = 63°
2 x + 20° = 2 ∙ 21° + 20° = 42° + 20° = 62°
x + 34° = 21° + 34° = 55°
The smallest exterior angle is 55°