Question

In Fig. lines $ AB$ and $ CD$ intersect at $ O$. If $ \angle AOC + \angle BOE = 70°$ and $ \angle BOD = 40°$, find $ \angle BOE$ and reflex $ COE$

Answer 1

Step 1: Find $\angle COE$

$AB$ is a straight line. Hence the sum of all angles on it is ${180}^{\circ }$

$\therefore$ $\angle AOC+\angle COE+\angle BOE={180}^{\circ }$

$\therefore$ $\angle COE={180}^{\circ }-{70}^{\circ }$

$\therefore$ $\angle COE={110}^{\circ }$

Step 2 : Find reflex $\angle COE$

Reflex $\angle COE={360}^{\circ }-\angle COE$

$\therefore$ Reflex $\angle COE={360}^{\circ }-{110}^{\circ }$

$\therefore$ Reflex $\angle COE={250}^{\circ }$

Step 3: Find $\angle BOE$

$CD$ is a straight line. Hence the sum of all angles on it is ${180}^{\circ }$

$\therefore$ $\angle COE+\angle BOE+\angle BOD={180}^{\circ }$

$\therefore$ $\angle BOE={180}^{\circ }-{110}^{\circ }-{40}^{\circ }$

$\therefore$ $\angle BOE={30}^{\circ }$

Hence the value of $\angle BOE$ is ${30}^{\circ }$ and the value of reflex $\angle COE$ is ${250}^{\circ }$.