Suppose ABCD is a rectangle whose diagonals AC and BD intersect at O. If ∠OAB=62∘, find ∠OBC
Open in App
Solution
The diagonals of a rectangle are equal and bisect each other. So, OA=OB
⟹∠OBA=∠OAB=62∘ (angles opposite to equal sides are equal) Since the measure of each angle of rectangle is 90∘ ⟹∠ABC=90∘ ⟹∠ABO+∠OBC=90∘ ⟹62∘+∠OBC=90∘ ⟹∠OBC=90∘−62∘=28∘