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