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In the figure given below, lines AB and CD intersect at O. If $∠ A O C + ∠ B O E = 70 °$ $and ∠ B O D = 40 °$ , then what are the values of $∠ B O E$ and reflex $∠ C O E$ ?

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∠ B O E = 30 ° and reflex ∠ C O E = ∠ 140 °

∠ B O E = 30 ° and reflex ∠ C O E = ∠ 250 °

∠ B O E = 40 ° and reflex ∠ C O E = ∠ 250 °

∠ B O E = 130 ° and reflex ∠ C O E = ∠ 140 °

answer is B.

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Detailed Solution

Given data:

∠ A O C + ∠ B O E = 70 °

∠ B O D = 40 °

Since AOB is a straight line, so the sum of all angles made on it is 180°.

⇒ ∠ A O C + ∠ C O E + ∠ E O B = 180 ° ...... (1)

∵ ∠ A O C + ∠ B O E = 70 ° ...... (2)

Substituting equation (2) in equation (1), we get.

70 ° + ∠ C O E = 180 ° ⇒ ∠ C O E = 110 °

Therefore, reflex

∠ C O E = 360 ° − 110 ° = 250 ° .

Since AB and CD intersect at O, therefore using the property of vertically opposite angles,

Substituting equation (3) in equation (2),

40 ° + ∠ B O E = 70 ° ⇒ ∠ B O E = 30 °

Therefore, the values of

and reflex

∠ C O E = 250 ° .

So, option (2) is correct.

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