Question

Match the figure at the right with the number that represents the sum of the interior angles for that figure.

Answer 1

To calculate the sum of the internal angles of a polygon you have to use the following formula:

`(n-2)\cdot180º`

Where "n" is the number of sides of the polygon.

So you have to subtract 2 to the number of sides of the polygon and then multiply the result by 180º to determine the sum of the interior angles.

1) The first polygon has n=4 sides. To calculate the sum of its interior angles you have to do as follows:

`\begin{gathered} (n-2)\cdot180º \\ (4-2)\cdot180º \\ 2\cdot180º=360º \end{gathered}`

2) The second polygon has n=5 sides. The sum of its interior angles can be calculated as:

`\begin{gathered} (n-2)\cdot180º \\ (5-2)\cdot180º \\ 3\cdot180º=540º \end{gathered}`

3) The third polygon has n=6 sides. You can calculate the sum of its interior angles as:

`\begin{gathered} (n-2)\cdot180º \\ (6-2)\cdot180º \\ 4\cdot180º=720º \end{gathered}`

4) The fourth polygon has n=7 sides, so you can calculate the sum of its interior angles as:

`\begin{gathered} (n-2)\cdot180º \\ (7-2)\cdot180º \\ 5\cdot180º=900º \end{gathered}`