Question

In the given figure, OC and OE are the bisector of ∠DOB and ∠AOD respectively. Then find the measure of ∠EOC.

Answer 1

Since OC bisects ∠DOB.
$\therefore \angle DOC=\angle COB=\frac{\angle DOB}{2}$ …..(i)
Similarly, OE bisects ∠AOD.
$\therefore \angle AOE=\angle EOD=\frac{\angle AOD}{2}$ …..(ii)
Now, ∠EOC = ∠EOD + ∠DOC
$=\frac{\angle AOD}{2}+\frac{\angle DOB}{2}$ [From (i) and (ii)]
$=\frac{1}{2}(\angle AOD+\angle DOB)$
$=\frac{1}{2}\times {180}^{\circ }$ $(\because \angle DOB\text{and}\angle AOD\text{from a linear pair})$
$={90}^{\circ }$
Hence, the required measure of ∠EOC is ${90}^{\circ }$