Answer:
D = 108°
F = 180°
H = 252°
I = 288°
Explanation:
Every regular polygon with n sides can be divided into n congruent triangles. The angle with vertex the center of the polygon will measure 360 : n degrees. This will also be the angle of rotation under which the polygon matches itself.
We are given a regular decagon, therefore:
n = 10
α = 360 : n = 36°
We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.
A' will coincide with D after three rotations: 3 × 36° = 108°
A' will coincide with F after five rotations: 5 × 36° = 180°
A' will coincide with H after seven rotations: 7 × 36° = 252°
A' will coincide with I after eight rotations: 8 × 36° = 288°
