Question

If the exterior angle of a regular polygon equals 120 degrees, what shape is the polygon?

Answer 1

A Triangle.

Explanation:

All the Exterior Angles of a polygon add up to 360°, so:

Each exterior angle must be `360°/n` (where n is the number of sides).

So, `360/n = 120` ; `n = 360/120 = 3` It is a triangle.

https://www.mathsisfun.com/geometry/regular-polygons.html

https://www.mathopenref.com/polygonexteriorangles.html

Answer 2

Triangle

Explanation:

What we are given is that there is a regular polygon with exterior angles that equal `120` degrees.

Any exterior angle added to its interior angle is equal to `180` degrees because they make a straight angle. Knowing this, we can calculate the measure of the interior angles:

`120 + x = 180`

`x = 60`

The measure of the interior angles of this polygon is `60` degrees.

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NOTE: (Although from this point you can intuitively understand that the polygon is a triangle because an equilateral triangle always has `3` interior angles that measure `60` degrees, I will continue the explanation to show the steps required to find the answer when it is not as obvious as this example.)

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From here we can modify the formula to find the total sum of the angles in a given regular polygon to better fit out purpose.

The original formula is:

`180(n-2) =`sum of all interior angles

We know that if we have `n` sides, there will be `n` number of angles. So we can modify the formula to find the sum of only one interior angle.

`(180(n-2))/n =`measure of ONE interior angle

Since we found the measure of the interior angles of this polygon, we can go ahead and substitute and solve for `n`, which is the number of sides this polygon has.

`(180(n-2))/n = 60`

`180(n-2)=60n`

`180n - 360 = 60n`

`120n = 360`

`n = 3`

Since we know that our polygon has `3` sides, we know that the polygon is a triangle.

Answer 3

Equilateral triangle.

Explanation:

In a regular polygon the sum of the exterior angles, one at each vertex is `360^o`. If there is one exterior angle at each vertex then the number of vertices`=` the number of sides.

Let `n=`number of sides. Then:

`n=360^o/120^o=3`

So the polygon is an equilateral triangle.