Question

Need help .... Regular octagon ABCDEFGH rotates 360 degree clockwise about it's center . After how many 45 increments will A' ( the image of the A coincide with F

Answer 1

Going from A to B means you've rotated 45 degrees. Then from B to C, you've gone 45 more degrees. So how many times do you have to do this to land on F?

B - 1×45 degrees
C - 2×45 degrees
D - 3×45 degrees
E - 4×45 degrees
F - 5×45 degrees

5×45 = 225 degrees

Answer 2

If the octagon is clockwise, then after 5 times 45 increments A' will coincide with F.

If the octagon is counterclockwise, then after 3 times 45 increments A' will coincide with F.

Explanation:

Case 1: Let the octagon is clockwise

It is given that a regular octagon ABCDEFGH rotates 360 degree clockwise about it's center.

There are 8 vertices and the central angle between two consecutive vertices is 45 degrees.

Central angle between AB is 45 degree.

Central angle between AC is

`\text{Angle between AB}+\text{Angle between BC}=45^(\circ)+45^(\circ)=2* 45^(\circ)`

Central angle between AD is

`\text{Angle between AB}+\text{Angle between BC}+\text{Angle between CD}=45^(\circ)+45^(\circ)+45^(\circ)=3* 45^(\circ)`

Similarly,

Central angle between AE is

`4* 45^(\circ)`

Central angle between FA is

`5* 45^(\circ)`

Therefore after 5 times 45 increments A' will coincide with F.

Case 2: Let the octagon is counterclockwise

`FA=AH+HG+GF`

`FA=45^(\circ)+45^(\circ)+45^(\circ)`

`FA=135^(\circ)`

`FA=3* 45^(\circ)`

Therefore after 3 times 45 increments A' will coincide with F.