Question

1. What is the measure of each interior angle of a regular pentagon?
2. Can you tile a floor with tiles shaped like regular pentagons? (ignore the difficulty in tiling along the edges of the room.)

Short answer

1. The measure of each interior angle of a regular pentagon is $\mathbf{108}\mathbf{°}$.
2. No, a floor cannot be tiled with tiles shaped like regular pentagons.

Step-by-step solution

Part a. Step 1. Write the formula to find the measure of each interior angle for a regular polygon with n sides.

The formula to find the measure of each interior angle of the regular polygon with sides is $\frac{\left(n-2\right)\mathbf{180}}{n}$.

Part a. Step 2. Find the value of n.

The number of sides in a pentagon is 5.

Therefore, the value of$n$ is 5.

Part a. Step 3. Calculate the measure of each interior angle for a regular pentagon.

The measure of each interior angle for a regular pentagon is given by:

$\begin{array}{c}\frac{\left(5-2\right)180}{5}=\frac{3\times 180}{5}\\ =3\times 36\\ =108\end{array}$

Therefore, the measure of each interior angle for a regular pentagon is $108°$.

Part b. Step 1. Definition of regular polygon.

A regular polygon is a polygon which has equal sides and equal angles.

Part b. Step 2. Description of step.

For tiling, the sum of angles around any vertex should be equal to $360°$.

Part b. Step 3. Write the conclusion.

The measure ofeach interior angle for a regular pentagon is $108°$.

As, 108 is not a factor of 360, therefore it is not possible to tile a floor with tiles shaped like regular pentagon.