A sporting goods store bought a ski set at a cost of $432. Later, the ski set was marked down 10% from its selling price and then marked down another 20%. The total markdown is the greatest possible markdown without the store losing money. Find the original selling price.

The original selling price of the ski set is $600

Step-by-step explanation:

The cost price of the ski set = $432

The first percentage mark down of the ski set = 10% from its selling price

The first percentage mark down of the ski set = 20% from its selling price

Let x represent the original selling price of the ski set at the sporting goods store, we are given;

80/100 × (90/100 × x) = The cost price of the ski set

Therefore, we have;

80/100 × (90/100 × x) = 432

0.72 × x = 432

x = 432/0.72 = 600

Therefore, the original selling price of the ski set, x = $600

∠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.