In the given figure, ABCD is a cyclic quadrilateral. What is the value of x∘50∘?
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Solution
We have, ∠CDA=180∘−80∘=100∘
and, ∠ABC+∠x=180∘ ∠ABC=180∘−x∘
Now, ∠CDA+∠ABC=180∘ [sum of opposite angles in a quadrilateral is 180∘] ⇒100∘+(180∘−x∘)=180∘⇒280∘−x∘=180∘ ⇒x∘=100∘ ∴x∘50∘=100∘50∘=2∘