Question

In Figure, lines AB and CD intersect at O. If \(∠\)AOC+\(∠\)BOE=70° and \(∠\)BOD=40°, find \(∠\)BOE and reflex \(∠\)COE.

Answer 1

Given:  

∠AOC + ∠BOE = 70° and ∠BOD = 40°

To Find:

∠BOE, and Reflex ∠COE

Solution:

From the figure, we know that lines AB and CD intersect at point O. The sum of angles on a straight line is 180°.

We can set up the following equation:

\[ \angle AOC + \angle BOE + \angle COE = 180^\circ \] and \[ \angle COE + \angle BOD + \angle BOE = 180^\circ \]

Substitute the given values:

\[ \angle AOC + \angle BOE + \angle COE = \angle COE + \angle BOD + \angle BOE = 180^\circ \] \[ 70^\circ + \angle BOE + \angle COE = \angle COE + 40^\circ + \angle BOE = 180^\circ \]

Now, we solve for ∠COE and ∠BOE:

\[ \angle COE = 110^\circ \] \[ \angle BOE = 30^\circ \]

Finally, to find the reflex ∠COE, we use:

\[ \text{Reflex} \, \angle COE = 360^\circ - 110^\circ = 250^\circ \]

Conclusion:

The values of the angles are:

• ∠BOE = 30°
• Reflex ∠COE = 250°