Question

question 18 of 25

you cannot tessellate seven-sided regular polygons by themselves.

a. true

b. false

Explanation:

Calculate the interior angle of a regular heptagon

Using the interior angle formula for a regular \(n\)-sided polygon:

$$ \theta = \frac{(n-2) \times 180^\circ}{n} $$

For a seven-sided regular polygon (\(n = 7\)):

$$ \theta = \frac{(7-2) \times 180^\circ}{7} = \frac{5 \times 180^\circ}{7} = \frac{900^\circ}{7} \approx 128.57^\circ $$

Determine if the interior angle divides 360 degrees

For a regular polygon to tessellate by itself, the interior angle must divide \(360^\circ\) without a remainder:

$$ \frac{360^\circ}{\theta} = \frac{360^\circ}{\frac{900^\circ}{7}} = \frac{360 \times 7}{900} = \frac{2520}{900} = 2.8 $$

Since \(2.8\) is not an integer, regular seven-sided polygons cannot tessellate by themselves.

Evaluate the statement

The statement "You cannot tessellate seven-sided regular polygons by themselves" is true.

Answer:

• A. True (Correct answer)
• B. False