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Question
In the given below Fig, find x. Further find ∠BOC, ∠COD and ∠AOD .
Solution
Since `∠`AOD and `∠`BOD are form a line pair
`∠`AOD + `∠`BOD = 180°
`∠`AOD + `∠`COD + `∠`BOC = 180°
Given that
`∠`AOD = ( x +10)°, `∠`COD = x°, `∠`BOC = ( x + 20)°
⇒ ( x +10)° + x° + ( x + 20)° = 180°
⇒ 3x + 30° = 180°
⇒ 3x = 180° - 30°
⇒ 3x = 150°
⇒ x = 50°
∴`∠`AOD = x +10°
= 50° +10° = 60°
`∠`COD = x° = 50°
`∠`BOC = x + 20° = 50 + 20 = 70°
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