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We are given that lines \(AB\) and \(CD\) intersect at point \(O\). The given conditions are:
- \( \angle AOC + \angle BOE = 70^\circ \)
- \( \angle BOD = 40^\circ \)

We are asked to find:
1. \( \angle BOE \)
2. Reflex \( \angle COE \)

### Step 1: Use the information about the linear pairs and supplementary angles
Since \(AB\) and \(CD\) are straight lines, the angles at point \(O\) form linear pairs, and their sum will always be \(180^\circ\).

From the diagram:
- \( \angle AOC \) and \( \angle BOD \) are supplementary, meaning:
\[
\angle AOC + \angle BOD = 180^\circ
\]
Substitute \( \angle BOD = 40^\circ \):
\[
\angle AOC + 40^\circ = 180^\circ
\]
\[
\angle AOC = 180^\circ - 40^\circ = 140^\circ
\]

### Step 2: Find \( \angle BOE \)
We are given that \( \angle AOC + \angle BOE = 70^\circ \). Substituting \( \angle AOC = 140^\circ \):
\[
140^\circ + \angle BOE = 70^\circ
\]
\[
\angle BOE = 70^\circ - 140^\circ = -70^\circ
\]
This negative result implies there's an error, as the sum cannot be less than zero. Would you like me to check over the diagram or proceed differently?

In figure given below, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

Learn how to find ∠BOE and the reflex angle ∠COE for the intersecting lines AB and CD at point O. This problem involves using the linear pair theorem and calculating angles around a point, suitable for students in Grades 7-9.

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