The sum of digits of s two digit number is 8. If 36 is added to this number, the digits are reversed. Find the number? (26)

The number is 26.

Step-by-step explanation:

Let the number be xy.

x + y = 8

10x + y  + 36 = 10y + x

9x - 9y = -36

Multiply the first equation by 9:

9x + 9y = 72

Adding this equation to the previous one:

18x = 36

x = 2

and y = 8 - 2 = 6.

6 on both sides and twelve on the top and the bottom

step-by-step explanation:

∠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.