If the exterior angle of a regular polygon equals 120 degrees, what shape is the polygon?
3 Answers
A Triangle.
Explanation:
All the Exterior Angles of a polygon add up to 360°, so:
Each exterior angle must be
So,
Triangle
Explanation:
What we are given is that there is a regular polygon with exterior angles that equal
Any exterior angle added to its interior angle is equal to
120 + x = 180
x = 60
The measure of the interior angles of this polygon is
NOTE: (Although from this point you can intuitively understand that the polygon is a triangle because an equilateral triangle always has
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
(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
(180(n-2))/n = 60
180(n-2)=60n
180n - 360 = 60n
120n = 360
n = 3
Since we know that our polygon has
Equilateral triangle.
Explanation:
In a regular polygon the sum of the exterior angles, one at each vertex is
Let
So the polygon is an equilateral triangle.