Given ray OC is perpendicular to ray OA and <DOA=135 degrees,what would be the measure of <DOC given that <COB=3x-7 and <BOA= -2x+4.

Anna/Susie -- please use the same name for your posts.

I'm getting x=138.Is that true?

not likely. How did you figure it?

If x=138, -2x+4 = -272

not likely one of the angles

Then I don't know how to do it.Can you please show me?I don't get it.

It seems that point B is irrelevant.

<AOC = 90
<AOD = 135
So, <COD = 45

As for finding x, it seems that
<COB + <BOA = 90
3x-7 + (-2x+4) = 90
x-3 = 90
x = 93
But that makes no sense, since then <BOA is negative.

If you lay out the diagram, with point A at the left, do points A,B,C,D progress left-to right?

If not, then describe the diagram more fully. Which are adjacent angles?

To find the measure of angle \<DOC, we need to use the given information and apply some geometric properties and theorems.

1. Start by drawing a diagram with the given information. Label the angles and points as stated in the question:

C-----------------------B
|
|
|
| O
|
|
D<A
Write the given angles:
\<DOA = 135 degrees
\<COB = 3x - 7
\<BOA = -2x + 4

2. Since ray OC is perpendicular to ray OA, we know that the sum of these two angles is 90 degrees. Thus,

\<DOC + \<DOA = 90 degrees

Substitute the given value into this equation:

\<DOC + 135 = 90

3. Solve the equation for \<DOC:

Subtract 135 from both sides:

\<DOC = 90 - 135

\<DOC = -45 degrees

Thus, the measure of angle \<DOC is -45 degrees.

Remember, angles can be negative when measured counterclockwise from a reference point.