Let AB and CD be two lines intersecting each other at O. If the ratio of ∠COB and ∠AOC is 5:4, then the measure of ∠AOD will be

90^o

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80^o

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120^o

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100^o

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Solution

The correct option is D
100^o

∠COB and ∠AOC form a linear pair of angles.

Let the angles be ∠COB = 5x and ∠AOC = 4x.

Then 5x + 4x = 180^o or x = 20^o

Thus ∠COB = 100^o and ∠AOC = 80^o.

Now, ∠COB and ∠AOD form a pair of vertically opposite angles.

Hence ∠AOD = ∠COB = 100^o

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