A single triangle is 180 degrees.
As you can see. Triangle A, as it is shown in the bad drawing. It is an isosceles triangle because two sides are equal to one another, indicated with the lines. Angle A is given as 57. By the isosceles triangle theorem, Angle A equals to Angle B. Calculating the missing angle: 180 - 57 (given) - 57 (because of the isosceles triangle theorem type of thing. I forgot) = 66
You can see it is a verticle angle so angle C is equal to angle D, therefore angle D is 66.
Again it is an isosceles triangle so Angle F is 66. 180 - 66(angle D) - 66(angle F) = 48 = angle x
Angle A = 57 degrees. Given
Angle A = Angle B. isosceles triangle theorem
Angle B = 57 degrees. Substitute
Angle A + Angle B + Angle C = 180. Definition of Triangle (I forgot what it was called)
57 + 57 + Angle C = 180. Substitution
Angle C = 66. Subtraction
Angle C = Angle D. Verticle angle theorem.
Angle D = 66. Substitution
Angle F = Angle D. isosceles triangle theorem
Angle F = 66. Substitution
Angle D + Angle F + Angle X = 180. Definition of Triangle?
66 + 66 + Angle X = 180. Substitution
Angle X = 48. Subtraction
