Final answer:
The angle ∠BOE is found to be 30° by using vertical angles and the given equation. The reflex angle ∠COE is calculated to be 320° by subtracting the straight angle measurement, and the value of ∠AOC from a full rotation.
Step-by-step explanation:
To find the angle ∠BOE when lines AB and CD intersect at O, we'll use the information provided:
∠AOC + ∠BOE = 70°
∠BOD = 40°
Since AB and CD intersect at O, we know by the properties of vertical angles that ∠AOC and ∠BOD are equal because they are opposite angles when two straight lines intersect. Therefore, ∠AOC = ∠BOD = 40°. Substituting the value of ∠AOC into the first equation,
40° + ∠BOE = 70°
Now we can solve for ∠BOE:
∠BOE = 70° - 40° = 30°
The reflex ∠COE is the larger angle that can be formed at the intersection which is supplementary to the straight angle (180°) with ∠AOC added:
Reflex ∠COE = 360° - ∠AOC = 360° - 40° = 320°
Therefore, ∠BOE is 30° and the reflex ∠COE is 320°.