Question

in figure-2 lines AC and BC in intersect at 0. if angle AOD:angleDOC=4:5 then find angle COB.
figure ​

Answer 1

To Find:-

The measure of ∠ COB

Given:-

• AC and BC intersect at O
• ∠ AOD and ∠ DOC is in a ratio of 4 : 5 respectively.

Solution:-

step-by-step explanation:

Let,

∠ AOD be 4x and ∠ DOC be 5x

We know that,

A straight angle always measures 180°

Therefore,

⟹ 4x + 5x = 180° ( linear pair )

⟹ 9x = 180°

⟹ x = 180/9

⟹ x = 20

The measure of the unknown angles:

⟹ 4x = 4 × 20 = 80

⟹ 5x = 5 × 20 = 100

So, ∠ AOD = 80° and ∠ DOC = 100°

So,

∠ COB = ∠ AOD ( opposite angles )

∠ DOC = ∠ AOB ( opposite angles )

So, ∠ COB = 80° and ∠ AOB = 100°

Required Answer:-

Now, Verification:-

∠ COB + ∠ AOD + ∠ DOC + ∠ AOB = 360°

⟹ 80° + 80° + 100° + 100° = 360°

⟹ 160 + 200 = 360

⟹ 360 = 360

L.H.S = R.H.S

Hence , Proved