Question

Sketch the polygon described. If no such polygon exists, write not possible.

A regular pentagon, one of whose angles has measure 120.

Short answer

Such a polygon described is not possible.

Step-by-step solution

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 for a regular polygon with sides is $\frac{\left(n-2\right)180}{n}$.

Step 2. Calculate the measure of each interior angle for a regular pentagon.

The number of sides in a pentagon is 5.

Therefore, the value of n is 5.

Therefore, the measure of each interior angle for a regular pentagon is given by:

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

Therefore, the measure of each interior angle for a regular pentagon is $180°$.

Step 3. Write the conclusion.

As, the measure of each interior angle for a regular pentagon is $180°$.

Therefore, the regular pentagon one of whose angle has measure 120 is not possible.