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Offline Centres

In the figure given below, AB, CD, and EF are three concurrent lines passing through the point O such that OF bisects $∠ B O D .$ If $∠ B O F = 35 °,$ If then what are the measures of $∠ B O C$ then what are the measures of and $∠ A O D$ and ?

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An Intiative by Sri Chaitanya

110 ° and 110 °

110 ° and 100 °

80 ° and 7 0 °

100 ° and 9 0 °

answer is A.

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Detailed Solution

It is given that AB, CD, and EF are three concurrent lines passing through the point O such that OF bisects

∠ B O D

such that

∠ B O F = 35 ° .

As OF bisects

∠ B O D,

therefore

∠ D O F = ∠ B O F ⇒ ∠ D O F = 35 °

Also, AB is a straight line and the sum of angles formed by a straight line is

180 ° .

∴ ∠ A O D + ∠ D O F + ∠ B O F = 180 °

⇒ ∠ A O D + 35 ° + 35 ° = 180 °

⇒ ∠ A O D = 180 ° − 70 °

⇒ ∠ A O D = 110 °

Since

∠ A O D

and

∠ B O C

are vertically opposite angles.

∴ ∠ A O D = ∠ B O C ⇒ ∠ B O C = 110 °

Therefore, the measure of

∠ A O D

110 °

and

∠ B O C

110 ° .

Hence, option (1) is correct.

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