Question

in the given figure if angle coe=2x°and angle bod=x° find where od id bisect of angle aob and oe is bisect of angle aoc​

Answer 1

Step-by-step explanation:

Given In the figure, OD LOE, OD and OE

are the bisectors of ∠AOC and ∠BOC

To show Points A, O and B are collinear

i.e., AOB is a straight line.

Proof Since, OD and OE bisect angles ∠AOC and ∠BOC, respectively.

∠AOC =2 ∠DOC ...(i)

and ∠COB = 2 ∠COE...(ii)

On adding Eqs. (i) and (ii), we get

∠AOC + ∠COB = 2 ∠DOC +2 ∠COE →

∠AOC +∠COB = 2(2DOC +∠COE)

→ ∠AOC + ∠COB= 2 ∠DOE

→ ∠AOC+ ∠COB = 2 x 90° [ OD 1 OE]

→ ∠AOC + ∠COB = 180°

→ ∠AOB = 180°

So, ∠AOC and ∠COB are forming linear pair.

Also, AOB is a straight line.

Hence, points A, O and B are collinear

$\huge{ son \: prodigal}$