Question

​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?​

Answer 1

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°