Question

Consider the following regular decagon. Choose the correct card to fill in the blanks below. 30° 36° 60 72° 5 10 15 20 of Rotating the decagon by a multiple of carries the decagon onto itself. Therefore, a rolation counterclockwise will carry the decagon onto itself. We can reflect the decagon different ways, including ways using the lines of symmetry that pass through the midpoints of two opposite sides. Which of the following is the correct sequence to fill in the blanks above?answersA. 30°, 60°, 10, 5B. 30°, 60°, 20, 10C. 36°, 72°, 5, 10D. 36°, 72°, 20, 10

Answer 1

The decagon can be divided in 10 equal parts, so if a full rotation is of 360º, a one tenth rotations will be of 360º/10= 36º

So if you rotate the decagon by a multiple of 36º the rotation will be onto itself, i.e. the figure will look as if it wasn't moved.

From the choices given, the angle that will rotate the angle counterclockwise onto himself will be multiple of 36º, the only one is 72º

This figure has 5 lines of symmetry that cross each vertex and 5 lines of symmetry that cross form the midpoint of one side to the midpoint of the oposite side. This is a total of 10 lines of symetry.

So you can reflect the decagon 10 different ways.

The correct choice is C: 36º, 72º, 10, 5