Question

jan wants to know why a regular pentagon will not tessellate the plane. how do you respond?
choose the correct answer below.
o a. a pentagon cannot be used to create a glide rotation because it has only one line of symmetry.
o b. each interior angle of a regular pentagon is 108°. if one puts three pentagons around a vertex, one gets 324°. what is left over is 36° and
cannot be an angle of another pentagon.
o c. a pentagon has no line of symmetry in which create a reflection. without reflecting, the tessellation cannot be created.
o d. fitting regular pentagons side-by-side results in pentagons sharing three vertices without rotation. the fourth and fifth vertex cannot be shared.

Explanation:

Step1: Recall tessellation condition

For a regular polygon to tessellate the plane, the interior angle must divide \(360^{\circ}\) evenly.

Step2: Analyze regular pentagon's interior angle

The interior angle of a regular pentagon is \(108^{\circ}\). Check \(360\div108=\frac{10}{3}\), which is not an integer.

Step3: Check option B

Option B explains that when three regular pentagons are around a vertex (\(3\times108 = 324^{\circ}\)), the remaining \(360 - 324=36^{\circ}\) cannot form another pentagon's angle. This correctly shows why regular pentagons don't tessellate.

Answer:

B. Each interior angle of a regular pentagon is \(108^{\circ}\). If one puts three pentagons around a vertex, one gets \(324^{\circ}\). What is left over is \(36^{\circ}\) and cannot be an angle of another pentagon.