Question

6. In the following figure, a = b = c. Name the angle which is
congruent to angle AOC.​

Answer 1

In figure, a=b=c

also, ∠AOB=a

∠BOC=b

∠COD=c

∠AOC=∠AOB+∠BOC=a+b⋯⋯(1)

Now ,a+b=c+b⋯⋯[∵a=b=c]

So, from figure,

a+b=c+b=∠COD+∠BOC=∠BOD⋯⋯(2)

hence, from (1) and (2)

∠AOC=∠BOD

That is ∠BOD is congrueBt of ∠AOC

Answer 2

Answer:

In figure, a=b=c

also, ∠AOB=a

∠BOC=b

∠COD=c

∠AOC=∠AOB+∠BOC=a+b⋯⋯(1)

Now ,a+b=c+b⋯⋯[∵a=b=c]

So, from figure,

a+b=c+b=∠COD+∠BOC=∠BOD⋯⋯(2)

hence, from (1) and (2)

∠AOC=∠BOD

That is ∠BOD is congrueBt of ∠AOC