Question

The sum of the exterior angles of a polygon is always 180 degrees.

True
or
False

Answer 1

false. it said ,"The sum of the exterior angles of a polygon is always 360 degrees. ... By an inductive proof, this is true for all polygons." that is what i think.

Answer 2

Option B

False

Explanation:

False, because

The sum of the exterior angles for each polygon is consistent for all types of polygons whether they are regular or irregular- no matter how many sides is always 360 degree.

for example:

Take any polygon, call it a square and show that a exterior angle of a square is 360 degree.

An exterior angle is formed by a side of the square and an extension of an adjacent side as shown below in the figure.

Let a, b, c and x are exterior angles.

We know that each interior angle in a square is equal to 90 degrees.

Interior angle + adjacent angle = 180°

90°+ x= 180°

or

x = 180°-90° = 90°

Since there are 4 exterior angles

therefore,
`4 * 90^(\circ)` = 360°

Therefore, the sum of the exterior angle of a square is 360°