Question

In the given figure, straight lines AB and CD intersect at O.

if angle AOC=40°
angle BOC=______

140°

60°

40°


​

Answer 1

Answer:

BOC=140° is correct answer,,,,,,,,,,,,,,,,,,,,,

Answer 2

$\bf\green{QuestioN:-}$

To find angle BOC in the given figure .

$\bf\red{AnsweR:-}$

140° is the correct answer.

ExplanatioN:-

In the given figure,

∠ AOC = 40°

AB & CD are two lines which intersect each other.

∴ ∠ AOC = ∠ BOD

   ∠ BOC = ∠ AOD

[ Vertically opposite angle]

And we know that,

Sum of these four angles = 360°.

ie,

∠AOC + ∠ BOC + ∠AOD + ∠ BOD = 360°.

We also know that,

∠ AOC = 40°

⇒ ∠ BOD = 40°

[ ∠AOC = ∠BOD]

Then,

⇒ ∠AOC + ∠ BOC + ∠AOD + ∠ BOD = 360°.

⇒ 40° +  ∠ BOC + ∠AOD + 40° = 360°.

⇒  ∠ BOC + ∠AOD + 80° = 360°.

⇒  ∠ BOC + ∠AOD  = 360°- 80°

⇒  ∠ BOC + ∠AOD  = 280°.

[ we know, ∠ BOC = ∠AOD ]

⇒ ∠ BOC + ∠AOD = 280°

⇒ ∠ BOC + ∠BOC = 280°

⇒ 2∠BOC = 280°

⇒ ∠BOC = 280°/2

⇒ ∠ BOC  = 140°.

Hence proved !!

All Done !!☺