In the adjoining figure, AB is parallel to CD. Find the value of x.
98∘
Draw a line parallel to AB and CD passing through O.
Now we know that interior angles on the same side of the transversal are supplementary
Therefore ∠BAO + ∠AOR = 180∘
⇒ ∠AOR + 130∘ = 180∘
⇒ ∠AOR = 50∘
and similarly
∠ROC + ∠OCD = 180∘
⇒ ∠ROC + 132∘ = 180∘
⇒ ∠ROC = 48∘
Hence
∠AOC = 50∘ + 48∘
⇒ ∠AOC = 98∘