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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

Respuesta :

kudzordzifrancis

Answer:

A) 40

Step-by-step explanation:

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

[tex](n - 2) \times 180[/tex]

For a hexagon, we put n=6

[tex](6 - 2) \times 180 = 4 \times 180 = 720[/tex]

Let x be the 6th interior angle, then

[tex]x + 110 + 120 + 90 + 140 + 125 = 720[/tex]

[tex]x + 585 = 720[/tex]

[tex]x = 720 - 585 = 135[/tex]

The largest interior angle is 140°

Therefore the least exterior angle will be:

[tex]180 - 140 = 40[/tex]

The correct choice is A

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