Hope’s mom bakes a cake for hope’s birthday. it is in the shape of a rectangle 10in. long and 6in. wide. if she starts at one corner and puts a candle every 2 inches, how many candles will fit around the edge of the cake?

16

Step-by-step explanation:

so we know the size of 2 edges or sides of the cake 6in and 10in, in a rectangle the opposite sides are the same, so there are 2 6in and 2 10in sides. add them together (6+6+10+10) to get 32in, now divide that by 2(the spacing of the candle) to get 16 candles around the edge.

∠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.