Question

ABCEDEFGH is a regular octagon. The minimum degree of rotation by which this octagon can map onto itself is . It will take increments of that degree of clockwise rotation for A’ (the image of A) to coincide with C.

Answer 1

45 or multiples of 45 around the centre of octagon

Explanation:

Given that ABCDEFGH is a regular octagon. i.e. it has 8 sides.

Since regular ocagon, all interior angles would be equal.

Sum of all interior angles of octagon = 2(8)-4 right angles

= 12 right angles

Hence each angle = 12(90)/8 = 135 degrees

Thus the octagon when rotated will take the same shape if vertices interchange also due to the property that all sides and angles are equal

Since each angle is 135 imagine an octagon with one vertex at origin O, and adjacent vertex B on x axis. OB has to be coincident with BC the next side or the previous side to get it mapped onto itself

The centre will be at the middle with each side subtending an angle of 45 degrees.

Hence if rotation is done around the centre with 45 degrees we will get octagon mapped onto itself.

45, 90, 135 thus multiples of 45