Question

Two lines AB and CD intersect at O. If $\angle AOC={50}^{\circ }$, find $\angle AOD,\angle BOD$ and $\angle BOC$.

Answer 1

We know that if two lines intersect then the vertically-opposite angles are equal.

Therefore, ∠AOC = ∠BOD = 50°

Let ∠AOD = ∠BOC = x°

Also, we know that the sum of all angles around a point is 360°.

Therefore,

∠AOC + ∠AOD + ∠BOD + ∠BOC = 360°

⇒ 50 + x + 50 + x = 360°

⇒ 2x = 260°

⇒ x = 130°

Hence, ∠AOD = ∠BOC = 130°

Therefore, ∠AOD = 130°, ∠BOD = 50° and ∠BOC = 130°.