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Question
Two straight line AB and CD intersect one another at the point O. If ∠AOC + ∠COB + ∠BOD = 274°, then ∠AOD =
Options
86°
90°
94°
137°
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Solution
Let us draw the following diagram showing two lines AB and CD intersecting at a point O.
Thus,
\[\angle \text { AOD}, \angle \text { AOC }, \angle \text { COB } \text { and } \angle \text { BOD }\] form a complete angle, that is the sum of these four angle is 360°.
That is,
It is given that
∠AOC + ∠COB +BOD = 274° ...(ii)
Subtracting (ii) from (i), we get:
∠AOD =360° - 274°
∠AOD = 86°
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