Properties of Parallelograms & Polygon Angles

Be sure to add your formulas to your formula sheet. "n" represents the number of sides.

A pentagon has 5 sides.

5 - 2 = 3, so there are 3 triangles inside a pentagon.

The angle sum in ONE triangle is $$180\degree$$ .

The angle sum for THREE triangles is

$$\left(5-2\right)180\degree=\ 540\degree$$

An octagon has 8 sides, with (8 - 2) triangles inside.

$$one\ interior\ angle\ =\frac{\left(n-2\right)180\degree}{n}$$

$$\frac{\left(8-2\right)180\degree}{8}$$

An octagon has 8 sides, with (8 - 2) triangles inside.

$$one\ interior\ angle\ =\frac{\left(n-2\right)180\degree}{n}$$

$$\frac{\left(8-2\right)180\degree}{8}$$

$$3960\degree=\left(n-2\right)180\degree$$

$$\frac{3960\degree}{180\degree}=n-2$$

$$22=n-2$$

$$n=24$$

$$\left(7-2\right)180\degree=900$$

add your 7 angles (x+90+148+140+136+142+150)

$$x+806=900$$

$$\left(6-4\right)180\degree=720\degree$$

add all the things (like terms)!

$$26x+278=720\degree$$

Consecutive angles are supplementary

$$180-72=108\degree$$

$$So,\ x+30=108$$

The diagonals of parallelograms bisect each other.

$$So...\ 3b-10=b+2$$

$$3b-b=2+10$$

$$2b=12$$

$$b=6$$