Final answer:
To find the measure of angle FGH, we solve the equation x + 75 = 180, which yields that angle FGH is 105 degrees.
Step-by-step explanation:
To find the value of x for the measure of angle FGH, we use the fact that the angles in a triangle sum up to 180 degrees. Since we have the measures of angles FGJ and JGH, we can express this relationship as:
FGH (x°) + FGJ (25°) + JGH (50°) = 180°.
By substituting the given angles, we find:
x + 25 + 50 = 180.
This simplifies to:
x + 75 = 180.
Subtracting 75 from both sides gives us:
x = 180 - 75.
Therefore, x = 105°.
The value of angle FGH is 105 degrees.