Question

match the figure at the right with the number that represents the sum of the interior angles for that figure. n=4 →n=5 →n=6 →n=7 →

Answer 1

We will match them by using the following expression:

`ia=(n-2)\cdot180`

Here ia represents the sum of all internal angles and n the number of sides of the shape.

*Now we solve for each shape in order:

1st. 4 sides:

`ia=(4-2)\cdot180\Rightarrow ia=360`

So, the first shape has a sum of internal angles that equals 360°.

2nd. 5 sides:

`ia=(5-2)\cdot180\Rightarrow ia=540`

So, the second shape has a sum of internal angles that equals 540°.

3rd. 6 sides:

`ia=(6-2)\cdot180\Rightarrow ia=720`

So, the third shape has a sum of internal angles that equals 720°.

4th. 7 sides:

`ia=(7-2)\cdot180\Rightarrow ia=900`

So, the fourth shape has