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Two lines AB and CD intersects at O. If $∠ A O C + ∠ C O B + ∠ B O D = 270 °$ , then the measure of $∠ A O D$ is:

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70 °

80 °

90 °

180 °

answer is C.

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Detailed Solution

Given a figure in which

∠ A O C + ∠ C O B + ∠ B O D = 270 °

Two lines A B and C D intersect at O . If ∠ A O C+∠ C O B+∠ B O D=270∘, then ∠ A O C=a 70∘b 80∘c 90∘d 180∘

By using angle sum property around point O,

∠ AOC + ∠ COB + ∠ BOD + ∠ AOD = 360 °

Now, putting the given values,

∠ AOC + ∠ COB + ∠ BOD = 270 °

Therefore,

⇒ ∠ A O D = 360 ° − 270 ° ⇒ ∠ A O D = 90 °

The measure of

∠ AOC = 90 °

.
Hence, option 3 is correct.

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