Question

In the adjoining figure, AOB is a straight line. Find the value of x. Hence, find $\angle AOC,\angle COD$ and $\angle BOD$.

Answer 1

AOB is a straight line. Therefore,

∠AOC + ∠COD + ∠BOD = 180°

⇒ 3x + 7° + 2x - 19° + x° = 180°

⇒ 6x = 192°

⇒ x = 32°

Therefore,

∠AOC = 3x = 3 × 32° + 7 = 103°

∠COD = 2x = 2 × 32° - 19 = 45°

and

∠BOD = x = 32°