Abcdefghij is a regular decagon. it rotates clockwise about its center to form the polygon a′b′c′d′e′f′g′h′i′j′. match each angle of rotation to the point that a′ (the image of a) coincides with after that rotation.

D = 108°

F = 180°

H = 252°

I = 288°

Step-by-step explanation:

The complete question is:

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

ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A′B′C′D′E′F′G′H′I′J′. Match each angle of rotation to the point that A′ (the image of A) coincides with after that rotation.

Tiles

252º

108º

135º

180º

288º

324º

Pairs

D

F

H

I

Solution:

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.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°

21

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.