Question

What is the relation between angleAOC,angleBOC,angleAOB

Answer 1

Answer:

Complete step-by-step answer:

Given, ∠AOC = ∠BOD and ∠AOB = 45∘. Also ∠BOD = 60∘

Now we have to find ∠BOC.

We are given that,

⇒ ∠AOC = ∠BOD-- (i)

From diagram it is clear that-

⇒ ∠AOB + ∠BOC = ∠AOC --- (ii)

Then substituting the values from eq. (ii) to eq. (i), we get,

⇒ ∠AOB + ∠BOC = ∠BOD

On putting the values of ∠AOB and ∠BOD, we get-

⇒45+∠BOC = 60

On transferring 45∘ from left side to right side, its sign changes and we get,

⇒∠BOC = 60 - 45

On subtraction we get,

⇒∠BOC = 15∘

Hence ∠BOC = 15∘ .

Note: In this question, the student may get stuck if he or she writes∠BOD=∠BOC + ∠COD in eq. (i) because we are not given the value of ∠BOC and ∠AOC in the question so split the angles into the only those angles whose value is given in the question, Otherwise the question cannot be solved. But if we were further asked to find ∠COD then it will be easy to find as we have already obtained the value of ∠COD because now we know the value of ∠BOC and the value of ∠BOD is already given so just put the values in the equation-

⇒∠BOD=∠BOC + ∠COD

We get,

⇒60=15 + ∠COD

Then on solving we get-

⇒∠COD=60−15=45

So ∠COD= ∠AOB = 45∘