Aregular 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

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

Thus, the correct option is (C) 1.