Question

Does any one know which of these go together?

Answer 1

For any n-sided (regular) polygon the interior angles are given by $180-\frac{360}{n}$

So for each shape listed:

Hexagon:
$180-\frac{360}{n}$
$180-\frac{360}{6}=120$

Decagon:
$180-\frac{360}{n}$
$180-\frac{360}{10}=144$

Pentagon:
$180-\frac{360}{n}$
$180-\frac{360}{5}=108$

Octagon:
$180-\frac{360}{n}$
$180-\frac{360}{8}=135$

Nonagon:
$180-\frac{360}{n}$
$180-\frac{360}{9}=140$

Heptagon:
$180-\frac{360}{n}$
$180-\frac{360}{7}=128\frac{4}{7}$