A motorboat goes downstream in a river and covers the distance between the coastal towns and 5 hours it covers a distance of stream in 6 hours if the speed of the stream is 2 km per hour find the speed of the boat in still water

∠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.

to find perimiter, add all the sides.

60 5/6 + 54 1/3 + 59 1/3 + 56 1/6.

goup like terms:

(60 5/6 + 56 1/6) + ( 54 1/3 + 59 1/3) = 117 + 113 2/3

56 + 60 =   116. 5/6 + 1/6 = 6/6 = 1/ 116 + 1 = 117

54 + 59 = 13. 1/3 + 1/3 =2/3. 13 + /3 = 113 2/3    

117 + 113 2/3 = 230 2/3

answer: 230 2/3