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In quadrilateral ABCD, it is given that angle A = angle C = 75° and angle B = angle D = 105°.
A student claims ABCD must be a parallelogram.
Is the claim correct and why?

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • ACorrect, both pairs of opposite angles are equal
  • BWrong, the angles do not total 360°
  • CWrong, equal angles do not imply parallelogram
  • DCorrect only if all sides equal

Step-by-Step Solution

Opposite angles equal (75=75 and 105=105) and they sum to 360, which is the condition for a parallelogram, so the claim is correct.
Answer: A) Correct, both pairs of opposite angles are equal

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