Question

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

  20
70
40
50

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=(80)/(2)\\\\\Rightarrow y=40.`

Thus, the value of y is 40.

Option (C) is CORRECT.