if m<DOA=83 degrees , m<DOC=2x+4 , m<BOA=15 degrees.what would x need to be to make ray oc an angle bisector of <DOB

just add up the angles...

15+2(2x+4) = 83

Would x=13?

No I'm sorry,would it be 15?

15+4x+8 = 83

4x = 60
x = 15

To find the value of x that would make ray OC an angle bisector of <DOB, we need to use the angle bisector theorem.

The angle bisector theorem states that in a triangle, if a line divides one interior angle into two angles of equal measure, then it divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides.

In this case, we have <DOA = 83 degrees and <BOA = 15 degrees. We want to find the value of x that would make ray OC an angle bisector of <DOB.

First, let's find the measure of <DOC using the given information. We are given that <DOA = 83 degrees and <BOA = 15 degrees. Since <DOC is an exterior angle of triangle DOA, we can find its measure by subtracting the measures of <DOA and <BOA from 180 degrees:

<DOC = 180 degrees - <DOA - <BOA
<DOC = 180 degrees - 83 degrees - 15 degrees
<DOC = 82 degrees

Now, according to the angle bisector theorem, if ray OC is an angle bisector of <DOB, then it divides side AB into two segments whose lengths are proportional to the lengths of segments AD and DB.

Let's assume that x is the measure of <DOC = 82 degrees. Since we are given that m<DOC = 2x + 4, we can substitute the value of x into the equation:

82 = 2x + 4

Now, let's solve this equation for x:

82 - 4 = 2x
78 = 2x
x = 78/2
x = 39

Therefore, to make ray OC an angle bisector of <DOB, x needs to be equal to 39.