To find the angle of any regular polygon you find the number of sides $\displaystyle n$. For a pentagon, $\displaystyle n=5$.

You then subtract 2 from the number of sides yielding 3.

Take 3 and multiply it by 180 degrees to yield the total number of degrees in the regular pentagon. $\displaystyle 3*180=540$

Then to find one individual angle we divide 540 by the total number of angles 5, $\displaystyle \frac{540}{5}=108$

The answer is $\displaystyle 108$.

The following equation can be used to determine the measure of an interior angle of a regular polygon, where $\displaystyle \small n$ equals the number of sides.

$\displaystyle \angle=\frac{180(n-2)}{n}$

In a pentagon, $\displaystyle \small n=5$.

$\displaystyle \angle=\frac{180(5-2)}{5}$

Now we can solve for the angle.

$\displaystyle \angle=\frac{180(3)}{5}=\frac{540}{5}=108^o$

The formula for the sum of the interior angles of a polygon is

$\displaystyle X=(s-2)(180^{\circ})$,

where $\displaystyle s$ is the number of sides in the polygon

Plugging in our values, we get:

$\displaystyle X=(5-2)(180^{\circ})$

$\displaystyle X=540^{\circ}$

Dividing the sum of the interior angles by the number of angles in the polygon, we get the value for each interior angle:

$\displaystyle \frac{X}{5}=\frac{540^{\circ}}{5}=108^{\circ}$

The measure of an interior angle of a regular polygon can be determined using the following equation, where $\displaystyle n$ equals the number of sides:

$\displaystyle \angle=\frac{180(n-2)}{n}$

$\displaystyle \angle=\frac{180(5-2)}{5}=\frac{180(3)}{5}=108$

The perimeter of a polygon is found by calculating the sum of all of the side lengths. In this instance, the polygon is regular, so the perimeter can be found by mulitplying the length of one side by the total number of sides:

$\displaystyle P=l\times n=6\times 5=30$

Use the Pythagorean Theorem to find the length of the diagonal:

$\displaystyle (\frac{1}{2}side)^2+(apothem)^2=(diagonal)^2$

$\displaystyle A^2+B^2 = C^2$

$\displaystyle (2\ m)^2+(2.75\ m)^2 = C^2$

$\displaystyle C\approx 3.4\ m$

Use the Pythagorean Theorem to find the length of the diagonal:

$\displaystyle (\frac{1}{2}side)^2+(apothem)^2=(diagonal)^2$

$\displaystyle A^2+B^2 = C^2$

$\displaystyle (3\ m)^2+(3\ m)^2=C^2$

$\displaystyle C=3\sqrt{2}\ m$

To find the side length of a regular pentagon with a perimeter of $\displaystyle 80$ you must use the equation for the perimeter of a pentagon.

The equation is $\displaystyle Perimeter=(side\: length)*(number\: ofsides)$

Plug in the numbers for perimeter and number of sides to get $\displaystyle 80=(side\: length)*(5)$

Divide each side of the equation by the number of sides to get the answer for the side length. $\displaystyle \frac{80}{5}=\frac{(side\: length)*(5)}{5}$

The answer is $\displaystyle \frac{80}{5}=16$.

The formula for the perimeter of a regular pentagon is

$\displaystyle P = 5(s)$,

where $\displaystyle s$ represents the length of the side.

Plugging in our values, we get:

$\displaystyle 30\ m=5(s)$

$\displaystyle s=6\ m$

The formula for the perimeter of a regular pentagon is

$\displaystyle P = 5(s)$,

where $\displaystyle s$ represents the length of the side.

Plugging in our values, we get:

$\displaystyle 20\ m = 5(s)$

$\displaystyle s=4\ m$