Question

The two figures above are regular. If s and t represent the lengths of the segments indicated in the figures, which statement is true?
A. s > t

B. t > s

C. s = t

D. No comparison can be made.

Answer 1

The answer:  s is greater than t ,, choice A

Explanation:

Each interior angle of a regular octagon = 135 degrees
Each interior angle of a regular hexagon = 120 degrees

Thus, ∠PBA = 67.5 degrees and ∠QNM = 60 degrees
In the octagon name the intersecting point of the altitude and the side; 'x'
In the hexagon name the intersecting point of the altitude and the side; 'y'
Consider the right triangles PBX and QNY
Now we can argue that the side opposite of the larger angle is going to be larger in those respective right triangles.