I have opened the image. Let me analyze the content and help you with the problem. It seems like there's a diagram and an associated geometry question.

I'll extract the relevant mathematical information and provide a solution for you.The problem involves geometry, specifically angles formed by intersecting lines. From the image, I can see the lines forming various angles around a point, with labels indicating points $A$, $B$, $C$, $D$, and $E$.

Here’s a breakdown of what I can infer from the image:

1. $\angle AOE$, $\angle COE$, $\angle DOA$, and other angles are being asked for measurements.
2. The given equation $m(\angle DOE) = m(\angle AOC)$, implies that these angles are congruent (i.e., they have equal measures).
3. There may be additional relationships between these angles (such as complementary or supplementary angles).

Could you clarify if you'd like me to find the angle measures for $m(\angle DOE)$, $m(\angle AOC)$, and any other angles shown? If so, I can provide more details.

Would you like me to proceed with any specific angle measurements or further clarifications?