Question

*Will fan and medal!* The sum of the measures of the interior angles of a convex polygon is 3060º. How many sides does the polygon have?

A. 17
B. 15
C. 19
D. 18

Answer 1

Looking at two simple examples: A quadrilateral can be divided into 2 triangles, but it has 4 sides.==> sum of interior angles = 180*2 = 360

A pentagon can be divided into 3 triangles, but it has 5 sides. ==> sum of interior angles = 180*3 = 540

You can generalize this for an n-sided polygon, so that the number of sides of a polygon is \[\frac{\text{sum of interior angles}}{180}-2=n\], where \(n\) is the number of sides on of the polygon.

Answer 2

ummm there is a slight error in to formula given

the angle sum of a polygon is

\[AS = (n - 2) \times 180\]

where AS = angle sum and n = number of sides in the polygon

to make n the subject...

divide both sides by 180

\[\frac{AS}{180} = n - 2\]

next add 2 to both sides of the equation

\[\frac{AS}{180} + 2 = n\]

now substitute AS = 3060 and then evaluate for n

hope it helps

Answer 3

Oh gosh good catch. I meant to write the negative two on the RHS, but then decided to just write it in terms of n and forgot to change the sign :\

Answer 4

Thanks