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.

Answer 1

A decagon has 10 sides.

It it is regular you can build 10 isosceles triangles from the center of the decagon to the 10 sides.

Each triangle has a common vertex where the angle of each triangle is 360° / 10 = 36°.

So each time that you rotate the decagon a multiple of 36° around the center you get an image that coincides with the original decagon.

If the letters are given clockwise:

- when you rotate 36° counter clockwise, the point A' (the image of A) will coincide with the point J.

- when you rotate 72° (2 times 36°) counter clockwise, the point A' will land on I.

- when you rotate 108° (3 times 36°) counter clockwise, the point A' will land on H.

- when you rotate 144° (4 times 36°) counter clockwise, the point A' will land on G.

- when you rotate 180° (5 times 36°) counter clockwise, the point A' will land on I.

- when you rotate 216° (6 times 36°) counter clockwise, the point A' will land on E.

- whn you rotate 252° (7 times 36°) counterclockwise, the point A' will coincide with D.

Add other 36° each time and A' will coincide successively with C, B and the same A.

Answer 2

Answer:

D -> 108

F -> 180

H -> 252

I -> 288

This was verified on Plato.

Step-by-step explanation:

There are 10 angles in a decagon so 360/10 = 36 degrees for each angle.  

B -> 36

C -> 72

and so on.