You have the following information:
m∠FCD = x + 41
m∠BCF = x + 78
m∠BCD = 95°
In order to find the value of x, you consider that the sum of the measure of angles ∠FCD and ∠BCF is equal to the measure of angle ∠BCD.
Thus, you have:
m∠FCD + m∠BCF = m∠BCD you replace by the given expressions
(x + 41) + (x + 78) = 95 you eliminate parenthesis
x + 41 + x + 78 = 95 simplify similar terms
x + x + 41 + 78 = 95
2x + 119 = 95 subtract 119 both sides
2x = 95 - 119
2x = -24 divide by 2 both sides
x = -24/2
x = -12
Hence, the value of x is - 12