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
[tex]m\angle EOF=y+30,\\\\m\angle FOG=3y-50.[/tex]
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
[tex]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.[/tex]
Thus, the value of y is 40.
Option (C) is CORRECT.
