In the adjoining figure, AOB is a straight line. Find the value of x. Also, find ∠AOC, ∠COD and ∠BOD.

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Solution

AOB is a straight line. Therefore,
$∠ A O C + ∠ C O D + ∠ B O D = 180 ° \Rightarrow (3 x + 7) ° + (2 x - 19) ° + x ° = 180 ° \Rightarrow 6 x = 192 ° \Rightarrow x = 32 °$
Therefore,
$∠ A O C = 3 \times 32 ° + 7 = 103 ° ∠ C O D = 2 \times 32 ° - 19 = 45 ° and ∠ B O D = 32 °$

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