Sophie's favorite number is a two-digit number. If she reverses the digits, the result is 45 less than her favorite number. The sum of the digits in her favorite number is 11. What is Sophie's favorite number?

83

Step-by-step explanation:

Why is the answer 83?

If the sum of the digits is 11, then this limits our answer options significantly. All of the following two-digit numbers have a sum of 11.

29, 92, 38, 83, 47, 74, 56, 65

Out of the numbers shown above, which follow the second hint?

If we took 92 and subtracted 29 from it, we would get 63.

If we took 83 and subtracted 38 from it, we would get 45.

This means that 83 is our answer.

i pretty sure it is

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)