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Determine whether the following regular polygon tessellates the plane. Explain.

-Decagon


Ayes; measure or interior angle = 144

Bno; measure of interior angle = 144

Cyes; measure of interior angle = 36

Dno; measure of interior angle = 36



Verified Answer :

NitroNida

The correct answer is B.) Measure of the Interior angle=144.

Answer:

The answer is option B

Step-by-step explanation:

A decagon cannot tessellate.

Tessellation means the tiling of a plane using geometric shapes with no overlaps or no gaps.

A regular polygon can only tessellate the plane if its interior angle divides 360 degrees. Hence, tessellation is only applicable for equilateral triangles, squares and regular hexagons. - NO DECAGONS

A decagon has an interior angle of 144 degrees. This when divided by 360 gives, \(\frac{360}{144}= 2.5\). We can see its not completely divisible and the answer is a fraction form. This is the reason decagon cannot tessellate.

Therefore, option B is the answer.

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