Question

A figure is a regular n-gon. Which of the following

expressions represents the sum of the measures of
the exterior angles of the polygon, one at each
vertex?
A. (180 - 10°
360
B. 180
12
C. (n - 2)180°
D. 360°

Answer 1

The correct answer is D. 360°

Explanation:

The sum of all the exterior angles of a regular n-gon or a polygon is always equal to 360°.

Let us consider the image attached.

First of all let us consider the triangle.

As per the property of exterior angles: The exterior angle is equal to the sum of 2 opposite interior angles.

`\Rightarrow \angle 1=\angle B + \angle C\\\Rightarrow \angle 2=\angle A + \angle C\\\Rightarrow \angle 3=\angle A + \angle B`

Where
`\angle A, \angle B\ and\ \angle C` are the interior angles of the triangle.

Adding the above equations:

`\angle 1 +\angle 2 +\angle 3 = 2 * (\angle A +\angle B +\angle C )`

The sum of interior angles of a triangle is always equal to 180°

`\angle A +\angle B +\angle C = 180^\circ`

`\angle 1 +\angle 2 +\angle 3 = 2 * 180^\circ\\\Rightarrow \angle 1 +\angle 2 +\angle 3 = 360^\circ`

Hence, proved that the sum of exterior angles is
`360^\circ`.

So, the correct answer is D.
`360^\circ`