Question

Instructions:Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

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°

Answer 2

I haven't seen  A, so I'm started with angle A as 36°

∠A = 36°
∠B = 36° + 36° = 72°
∠C = 72° + 36° = 108
∠D = 108° + 36° = 144°
∠E = 144° + 36° = 180°
∠F = 180° + 36° = 216°
∠G = 216° + 36° = 252°
∠H = 252° + 36° = 288°
∠I = 288° + 36° = 324°
∠J = 324° + 36° = 360°