Final answer:
After setting up an equation based on the sum of angles around a point being 360 degrees, the solution for x is -12, which does not match any of the provided answer choices, suggesting there is an error in the problem setup.
Step-by-step explanation:
To find the value of x using the given angles in the question, we should recognize that the sum of angles around a point is 360 degrees. Assuming points F, C, and D as well as points B, C, and F are connected lines forming two angles sharing a common vertex and side, we can use the given angles to set up the equation:
m∠ FCD + m∠ BCF = m∠ BCD
(x + 41) + (x +78) = 95
Now, we add the expressions on the left side:
2x + 119 = 95
Then, we subtract 119 from both sides to solve for x:
2x = 95 - 119
2x = -24
Divide both sides of the equation by 2:
x = -24 / 2
x = -12
However, none of the answer choices match our solution, indicating that there might have been an error or misinterpretation in the setup of the problem as it relates to the given angles.