If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?
the sum for the exterior angles of any polygon is 360°
so solve
180(n-2) = 360
180n - 360 = 360
180n = 720
n = 4
looks like a quadrilateral
To determine the number of sides of a convex n-gon, you need to understand some properties of polygons.
The sum of the measures of the interior angles of any n-gon is given by the formula:
Sum of Interior Angles = (n - 2) * 180 degrees.
The sum of the measures of the exterior angles of any convex polygon is always 360 degrees.
Now, let's solve the problem step by step:
1. Let's assume that the number of sides of the n-gon is "n".
2. According to the given condition, the sum of the measures of the interior angles of the n-gon is equal to the sum of the measures of the exterior angles. Therefore, we can write the equation:
(n - 2) * 180 = 360
3. Now, let's solve the equation:
Divide both sides of the equation by 180:
(n - 2) = 2
Add 2 to both sides of the equation:
n = 4
4. Hence, the n-gon has 4 sides.
So, the n-gon is a quadrilateral, commonly known as a square when all four sides are equal.