Question

The measure of 5 of the interior angles of a hexagon are 110, 120, 90, 140, and 125. what is the measure of the smallest exterior angle?

A) 40
B) 45
C) 30
D) 35

Answer 1

A) 40

Explanation:

The sum of the interior angles of a regular polygon is:

`(n - 2) * 180`

For a hexagon, we put n=6

`(6 - 2) * 180 = 4 * 180 = 720`

Let x be the 6th interior angle, then

`x + 110 + 120 + 90 + 140 + 125 = 720`

`x + 585 = 720`

`x = 720 - 585 = 135`

The largest interior angle is 140°

Therefore the least exterior angle will be:

`180 - 140 = 40`

The correct choice is A