Question

ABCD is a rectangle whose diagonals AC and BD intersect at point O such that ∠B0C = 60°. Find the measure of ∠0DC.

Answer 1

Answer:

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

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