Question

It is given that OD and OE are the bisectors of angle AOC and angle BOC respectively, OD is perpendicular to OE and angle AOD : angle BOE = 1 : 2. What is the measure of

Answer 1

Given In the figure, OD ⊥ OE, 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. So, ∠AOC and ∠COB are forming linear pair.

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Answer 2

Answer:

Given In the figure, OD ⊥ OE, 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(∠DOC +∠COE)

⇒ ∠AOC + ∠COB= 2 ∠DOE

⇒ ∠AOC+ ∠COB = 2 x 90° [∴ OD ⊥ 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.