In the given figure, AB and CD are two lines intersecting at O. If ∠AOC and ∠BOC are in ratio 2 : 3, find all angles.
72∘,108∘,108∘,72∘
∠AOC+∠BOC=180∘ [Linear Pair]
∠AOC:∠BOC=2:3
Let ∠AOC=2x and ∠BOC=3x
⇒2x+3x=180∘
⇒5x=180∘
⇒x=36∘
Thus, ∠AOC=2x=72∘And ∠BOC=3x=108∘
∠BOD=∠AOC=72∘
∠AOD=∠BOC=108∘