Question

 bisects EOG. EOF = y + 30 and FOG = 3y – 50. Solve for y. 20704050

Answer 1

Since given it bisects EOF must be equal to FOG

y+30 = 3y-50

2y = 80

y = 40

Answer 2

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.