Question

question 6 of 10 its possible to create a regular tessellation with a regular octagon. a. true b. false

Explanation:

Step1: Calculate the interior angle of a regular octagon

The formula for the interior angle of a regular polygon is \(\theta=\frac{(n - 2)\times180^{\circ}}{n}\), where \(n = 8\) (for an octagon). So \(\theta=\frac{(8 - 2)\times180^{\circ}}{8}=\frac{6\times180^{\circ}}{8}=135^{\circ}\).

Step2: Check the tessellation condition

For a regular tessellation, the interior angle \(\theta\) of the regular polygon must satisfy \(360^{\circ}\div\theta = k\) (where \(k\) is an integer). Since \(360^{\circ}\div135^{\circ}=\frac{8}{3}\), which is not an integer, a regular octagon cannot form a regular tessellation.

Answer:

B. False