Two cars leave towns 510 kilometers apart at the same time and travel toward each other. One car's rate is 14 kilometers per hour less than the other's. If they meet in 3 hours, what is the rate of the slower car?
Do not do any rounding.

time = 3 hours

speed = distance / time

2x+18 = 510/3

2x+18= 170

2x= 170-18

2x= 152

x= 152 /2

x= 76 km/h

add 18 to x to find the speed of the other car

∠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.