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Question
In the following figure, find the value of ∠BOC, if points A, O and B are collinear.
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Solution
Since, A, O and B are collinear.
Then, AOB will be a straight line and sum of all the angles on a straight line is 180°.
∴ ∠AOD + ∠DOC + ∠COB = 180°
⇒ (x – 10)° + (4x – 25)° + (x + 5)° = 180°
⇒ x – 10° + 4x – 25° + x + 5 = 180
⇒ 6x – 30° = 180°
⇒ 6x = 180° + 30°
⇒ 6x = 210°
⇒ x = 35°
Now, ∠BOC = (x + 5)°
= (35 + 5)°
= 40°
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