The value of x is 57
To find the value of angle x in a triangle with one angle given (66 degrees), one can use the fact that the sum of all angles in a triangle is always 180 degrees.
Let the angles of the triangle be A, B, and C, where angle A is 66 degrees. The sum of all angles is:
A + B + C = 180
Now, plug in the known value:
66 + B + C = 180
To find angle x (which is angle B), you'll need to isolate B:
B = 180 - 66 - C
Since x is another name for angle B, you can say:
x = 180 - 66 - C
x = 114 - C
Since the value belongs to the two angles remaining, then to solve the real value of x and C, divide it by 2.
x = 114/2
x = 57
In order to get the value for C, then, return to the first formula
A + B + C = 180 (sum of angles in a triangle)
66 + 57 + C = 180
123 + C = 180 (collect like terms)
C = 180 - 123
= 57
Therefore, considering the fact that the sum of all angles in a triangle is always 180 degrees, then A (66) + x (57) + C (57) = 180. We can then conclude that x is 57.