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Two lines AB and CD intersect at O. If AOC={50}^{o}, find AO

Question

Two lines $A B$ and $C D$ intersect at $O$ . If $∠ A OC = 50^{o}$ , find $∠ A O D, ∠ BO D$ and $∠ BOC$

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Jack Discussed

Two lines

A B

and

C D

intersect at

O

. If

∠ A OC = 50^{o}

, find

∠ A O D, ∠ BO D

and

∠ BOC

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

From the figure we know that

∠ A OC

and

∠ A O D

from a linear pair

It can also be written as

∠ A OC + ∠ A O D = 180^{o}

By substituting the values

50^{o} + ∠ A O D = 180^{o}

∠ A O D = 180^{o} - 50^{o}

∠ A O D = 130^{o}

According to the figure we know that

∠ A O D

and

∠ BOC

are vertically opposite angles

So we get

∠ A O D = ∠ BOC = 180^{o}

According to the figure we know that

∠ A OC

and

∠ BO D

are vertically opposite angles

So we get

∠ A OC + ∠ BO D = 50^{o}

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Question Text	Two lines $A B$ and $C D$ intersect at $O$ . If $∠ A OC = 50^{o}$ , find $∠ A O D, ∠ BO D$ and $∠ BOC$
Answer Type	Text solution:1
Upvotes	150

Two lines AB and CD intersect at O. If ∠AOC=50o, find ∠AOD, ∠BOD and ∠BOC

Text solutionVerified

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Two lines $A B$ and $C D$ intersect at $O$ . If $∠ A OC = 50^{o}$ , find $∠ A O D, ∠ BO D$ and $∠ BOC$