Question

A regular pentagon shares a common center with a regular hexagon. If LM¯¯¯¯¯ || AB¯¯¯¯¯, across how many lines of reflection can the combined figure be reflected to map onto itself? A. 6 B. 3 C. 1 D. 0

Answer 1

In your question here where as a regular pentagon shares a common center with a regular hexagon and if LM is congruent AB, the possible lines of reflection that the combined figure reflected to map itself is A. 6. I hope your are satisfied with my answer and feel free to ask for more 

Answer 2

Answer: The answer is (C) 1.

Step-by-step explanation: As drawn in the attached figure and given in the question, LMNOPQ is a regular hexagon and ABDEF is a regular pentagon, both of them have same centre 'C'.

We are to find the number of lines of reflection across which the combined figure will be reflected onto itself.

Now, a regular hexagon is symmetric at an angle of 60° and a regular pentagon is symmetric at an angle of 72°.

Therefore, the combined figure will be symmetric at angle

= LCM (60°, 72°) = 360°.

So, number of lines of reflection will be

$n=\dfrac{360^\circ}{360^\circ}=1.$

Thus, the correct option is (C) 1.