Question

Regular octagon ABCDEFGH rotates 360 degrees clockwise about its center. After how many 45 degree increments will A' coincide with F?

8

4

5

3

Answer 1

Given that the octagon rotates 360 degrees, it is a given that for every regular division of the polygon (360/8 = 45 degrees), the image would coincide with the pre-image during the rotation. Therefore, the octagon would coincide a total of 8 times as it rotates 360 degrees about its center.

Answer 2

Option D. 3

Explanation:

A regular ABCDEFGH rotates 360° clockwise about its center.

It means if A coincides H, if A moves
`(360)/(8)=` 45° clockwise.

Now we can say that A will coincide the point F if A rotates 3 times by 45° clockwise.

In other words, if A rotates (3×45° = 135°) clockwise, point A will coincide point F.

Therefore, Option D. 3 will be the answer.