Chapter 11.3, Problem 22IP

To determine

To determine whether or not a tessellation can be created.

Answer to Problem 22IP

No

Explanation of Solution

Given:

15-gon

Formula used:

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

A 15-gon has 15 sides, $n=15$

  $\Rightarrow$ The measure of one interior angle $=\frac{\left(15-2\right)\times 180}{15}$

  $\Rightarrow$ The measure of one interior angle $=\frac{13\times 180}{15}$

  $\Rightarrow$ The measure of one interior angle $=\frac{2340}{15}$

  $\Rightarrow$ The measure of one interior angle $=156°$

Each interior angle of a quadrilateral measures $156°$ and $360°$ is not evenly divisible by $156°.$

Conclusion:

Therefore, the given quadrilateral is not a tessellation.