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

Answer:

A) 40

Step-by-step explanation:

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

$(n - 2) \times 180$

For a hexagon, we put n=6

$(6 - 2) \times 180 = 4 \times 180 = 720$

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