Decagon is a regular polygon with 10 sides. The correct option that fills up the blanks is given by: Option C: 36°, 72°, 10, 5
What is a decagon?
A decagon is a regular polygon with 10 sides.
As shown in the diagram attached below, the angle between two line segments connecting center and two adjacent vertex is of 36°.
Since rotating the decagon by that angle will land it in an unidentifiable way, as it looks alike, thus, rotating the decagon by a multiple of __36°__ carries the decagon onto itself.
Therefore, a rotation of _36 degree or 72 degree or any multiple of 36 degree__ counterclockwise will carry the decagon onto itself.
If we connect one vertex to opposite one, and flip it on that connecting line(this flip is called reflection), then the decagon will look same as before reflection.Thera are 5 such different lines.
Now in addition, we can connect lines from mid point of 1 side to other opposite side too. And this also can be done in 5 ways. On these connecting lines too, the decagon can be reflected onto itself.
Thus, we can reflect the decagon _5+5=10_ different ways. (these are the only ways, and it can be proven mathematically).
And including __5__ ways using the lines of symmetry that pass through the midpoints of two opposite sides
Thus, the correct option that fills up the blanks is given by: Option C: 36°, 72°, 10, 5
Learn more about reflection symmetry here:
https://brainly.com/question/7783612
