27 A two digit number is such that the sum of digits is 13. When digits are
reversed, original number is increased by 9. Find the original number.​

The original nimber is 67.

Step-by-step explanation:

Let the two digits be x and y.

According to the question.

The sum of two digits of a two digit number is

x + y = 13

or, x = 13 - y

And, a two digit number can be written as

x × 10 + y

when the digits are reversed, the number can be written as

y × 10 + x

the original number increases by 9. i.e.

y x 10 + x = x × 10 + y + 9

Replacing value of x by 13 - y,

y × 10 + 13 - y = 10(13 - y) + y + 9

10y + 13 - y = 130 - 10y + y + 9

9y + 13 = 139 - 9y

18y = 139 - 13

18y = 126

y = 126/18

y = 7

So, x = 13 - y

= 13 - 7

= 6

The original number is x × 10 + y = 6 x 10 + 7 = 67.

∠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.