Question

PLEASE HELP ME WITH THIS
THX
PLZ EXPLAIN
15 PTS

Answer 1

A regular decagon has 10 sides. The central angle is equally divided into 10, which is 360/10=36 ° between adjacent diagonals.

This also means that a rotation of 36 ° will create an image identical to the preimage, except for letter labels. The order of rotational symmetry is therefore 10, with angles of rotations in multiples of 36 ° .

Thus, A' coincides with B, the rotation angle is 36 °. If A' coincides with C, the rotation is 36*2=72 ° and so on.

So the number of letter spaces between A and the destination letter, multiplied by 36 ° gives the rotation angle, in this case, clockwise, since this is how the letters are numbered.

Back to the question,

Vertex letter spaces angle

D 3 * 36=108 °

F 5 * 36=180 °

H 7 * 36=252 °

I 8 * 36=288 °

Answer 2

Step One

The first thing to do is make a table of how many letters "A" will go through to get to it's destination. In order to do this,, you need to realize that the angular distance between letters is 36 degrees. So if the center of the circle is O, then AOB = 36 degrees. How did I get that? The figure is a decagon. That means it has 10 equal divisions going from A to J. 360 / 10 = 36 degrees between each letter.

Angle Positions Moved

252............................7

108.............................3

135 ...........................3.75 I can't see how this will be an answer. It is between the 3rd and 4th letters, so there is no letter sitting in that place.

180.............................5

288............................8

324 ...........................9

Step Two

How will A land on D? Start with B. It counts as 1. Now go to C that counts as 2. Finally you hit D on the third angle. For D you put in 108 degrees.

You do each of the other letters the same way. Make up another table

Letter Angle # Steps

D ................108 ................3

F.................180 ................5

H................252.................7

I.................288.................8

This is a pretty nice little problem.