A roller skater was skating on a road. The skater covered some distance before coming to a stop. The number of rotations of the skating wheel was found to be 6. If the radius of the wheel is 10 cm, find the distance covered by the skater (in cm). Leave the answer in terms of pi.

The distance covered by the skater is 120π cm.

Step-by-step explanation:

Since we have given that

Radius of wheel = 10 cm

Number of rotations of the skating wheel = 6

According to question, we get that

Hence, the distance covered by the skater is 120π cm.

∠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.