Interior Angle of an N-gon

By: Karl Luigi D. Extra

Rey Joseph A. Velasquez

Marivic suggests a different way to find the sum of the measures of the interior angles of an n-gon. She picks an interior point of the figure, draws segments to each vertex, counts the number of triangle, multiplies by , then subtracts 360. Will her method work?

Proving no. 1:

Marivic’s way:

A quadrilateral has four interior angle. If Marivic will multiply it by 180 the product will be 720, and if she will subtract 360 to the product the difference is 360. So the sum of the measures of the interior angles of a quadrilateral is 360.

Our solution:

Our teacher said that in order to find the sum of the measures of the interior angles we need to subtract the number of sides by 2, and multiply the difference by 180. So if a quadrilateral has four sides and if we will use the equation that our teacher taught to us; the difference if we subtract 2 to the number of sides of a quadrilateral is 2, and if we will multiply it by 180 the product will be 360. So the sum of the measures of the interior angles of a quadrilateral is 360.

Proving no. 2:

Marivic’s formula:

Sum of the measures of the interior angles of an n-gon is equal to n(180)-360 where n = no. of triangles of a polygon.

Our formula:

Sum of the measures of the interior angles of an n-gon is equal to n-2(180) where n = no. of sides of a polygon.

Presentation:

If the formula that Marivic use will be equal to the formula that our teacher taught to us, then her formula is correct.

n(180)-360 = n-2(180)

180n-360 = 180n-360