Answer: the correct option is (C) 40.
Step-by-step explanation: As shown in the attached figure below, the line OF bisects the angle EOG, where
\(m\angle EOF=y+30,\\\\m\angle FOG=3y-50.\)
We are to find the value of y.
Since OF is the bisector of the angle EOG, so it divides the angle EOG into two congruent angles.
Therefore, we get
\(m\angle EOF=m\angle FOG\\\\\Rightarrow y+30=3y-50\\\\\Rightarrow 3y-y=30+50\\\\\Rightarrow 2y=80\\\\\Rightarrow y=\dfrac{80}{2}\\\\\Rightarrow y=40.\)
Thus, the value of y is 40.
Option (C) is CORRECT.
