Question

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

-Decagon


a. yes; measure or interior angle = 144

b. no; measure of interior angle = 144

c. yes; measure of interior angle = 36

d. no; measure of interior angle = 36

Answer 1

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

Answer 2

The answer is option B

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,
`(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.