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Question

In the given figure, if AOC and BOC are in ratio 2 : 3, find AOC, COB, BOD and AOD.


A

72,108,72 and 108

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B

45,100,45 and 100

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C

30,30,120 and 120

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D

50,120,50 and 120

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Solution

The correct option is A

72,108,72 and 108


Given: AOC:BOC=2:3
Let measure of AOC and BOC be 2x and 3x.
Here, AOC and BOC form a linear pair of angles.
AOC+BOC=180
2x+3x=180
5x=180
x=36

AOC=2x=2×36=72
BOC=3x=3×36=108

We know that when two lines intersect, the vertically opposite angles are equal.
BOD=AOC=72
AOD=BOC=108


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