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

C. 1

Explanation:

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=(360^\circ)/(360^\circ)=1.`

Thus, the correct option is (C) 1.