The sum of the interior angles of a triangle is 180 degrees, of a quadrilateral is 360 degree and of a pentagon is 540 degrees.

Question

The sum of the interior angles of a triangle  is 180 degrees, of a quadrilateral is 360 degree and of a pentagon is 540 degrees.

 

A. Write a rule to model this situation

 

B. Assuming this pattern continues, find the sum of the interior angles of a 15-sided figure.

 

C. Explain why an arithmetic sequence is the best way to model this situation. Explain the relationship between the number of sides and the nth term.

Answer 1

3 sides  180 degrees

4 sides  360 degrees

5 sides  540 degrees

 

You can see that for each additional side the degrees are increasing by 180. In an arithmetic sequence difference between two consecutive terms is always same.

 

For 5 sides the term is 5*180 + C (where c is a constant)

5*180 + C = 540 => 900 + C = 540 or C = -360

 

Use this formula for 3 sides you get -360 + 3*180 = -360 + 540 = 180

For four sides -360 + 180*4 = 360

 

For a object with n sides it is -360 + n*4

Since -360 = -2*(180)

 

The general formula is also written as (n-2)*180

 

For a fifteen sided share the sum of angles = (15-2)*180 = 13*180