In the given figure, if ∠AOC and ∠BOC are in ratio 2 : 3, find ∠AOC, ∠COB, ∠BOD and ∠AOD.
72∘,108∘,72∘ and 108∘
Given: ∠AOC:∠BOC=2:3
Let measure of ∠AOC and ∠BOC be 2x and 3x.
Here, ∠AOC and ∠BOC form a linear pair of angles.
⇒∠AOC+∠BOC=180∘
⇒2x+3x=180∘
⇒5x=180∘
⇒x=36∘
∴∠AOC=2x=2×36∘=72∘
∠BOC=3x=3×36∘=108∘
We know that when two lines intersect, the vertically opposite angles are equal.
⇒∠BOD=∠AOC=72∘
⇒∠AOD=∠BOC=108∘