Question

ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A′B′C′D′E′F′G′H′I′J′. Match each angle of rotation to the point that A′ (the image of A) coincides with after that rotation.

252º
108º
135º
180º
288º
324º
D

F

H
I

Answer 1

See the explanation.

Explanation:

ABCDEFGHIJ is a regular decagon, that is all the sides are equal or constant.

All the vertex of the decagon creates an angle of 360 degree at the center of the polygon.

Hence, if the Decagon will be rotate 360 degree, in any direction, the points will be coincides with itself after rotation.

So, we can consider that each side creates an angle of 36 degree at its center.

Lets put the points of the decagon in a clock wise direction [Put the points in the given sequence in clock wise direction].

At the rotation of 252 degree, the point A cross
`(252)/(36) = 7` sides. After crossing one side A′ will coincide with B. Similarly, for two sides it will coincide with C. Hence, after crossing 7 sides, A′ will coincides with H.

At the rotation of 108 degree, the point A cross
`(108)/(36) = 3` sides. Hence, A′ will coincides with D this time.

At the rotation of 135 degree, the point A cross
`(135)/(36) = 3.75` sides. Hence, A′ will lie between D and E, nearer to E.

After 180 degree rotation, the point A will cross
`(180)/(36) = 5` sides. Hence, after rotation A′ will coincide with F.

Rotating 288 degree, A will be able to cross
`(288)/(36) = 8` sides. Thus, A′ will coincide with I.

Rotating 324 degree, A will be able to cross
`(324)/(36) = 9` sides. Thus, A′ will coincide with J.