Question

Ray OD stands on line AOB.If ray oc and OE bisects angle BOD and angle AOD respectively. Find the angle COE

Answer 1

therefore, angle coe =90

Answer 2

The measure of ∠COE is 90°

 

Step-by-step explanation:

Given:

Here Ray OD stands on line AOB.

And ray OC and OE bisects ∠BOD and ∠AOD respectively.

To find: The measure of ∠COE?

Now,

Ray OD stands on line AOB

then, ∠BOC + ∠AOC = 180°    [linear pair]

Dividing throughout by 2, we get

⇒ $\frac{1}{2} \angle BOC + \frac{1}{2} \angle AOC = \frac{180}{2}$

⇒ $\frac{1}{2} \angle BOC + \frac{1}{2} \angle AOC = \frac{90}{2}$      [1]

Now, OC is the bisector of ∠BOD and OE is the bisector of ∠AOD respectively then,

∠COD = ∠BOC    

⇒ $\frac{1}{2}$ ∠BOD = ∠COD       [2]

and ∠EOD = ∠EOA

⇒ $\frac{1}{2}$ ∠AOD = ∠EOD          [3]

then, adding (2) & (3)

$\frac{1}{2} \angle BOD + \frac{1}{2} \angle AOD = \angle COD + \algle EOD$            [4]

Now,  from (1) & (4), we get,

$\frac{1}{2} \angle BOD + \frac{1}{2} \angle AOD = \angle COD + \algle EOD$

90° = ∠COD + ∠EOD

⇒∠COE = 90°