Question

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

A regular polygon, one of whose angles has measure 130.

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 number of sides of the regular polygon which has each interior angles measuring 130.

The measure of each interior angle for a regular polygon is given as 130.

Therefore, the value of can be obtained as:

$$\begin{gathered} \frac{\left(n-2\right)180}{n}=130 \\ \left(n-2\right)180=130n \\ 180n-360=130n \\ 180n-130n=360 \\ 50n=360 \\ n=\frac{360}{50} \\ n=7.2 \end{gathered}$$

Therefore, the number of sides in the regular polygon having each interior angle measuring 130 is 7.2.

Step 3. Write the conclusion.

As, the number of sides in the regular polygon having each interior angle measuring 130 is 7.2

That is the number of sides is fractional, which is not possible.

Therefore, the regular polygon one of whose angle has measure 130 is not possible.