Question

Adjacent angles of a parallelogram are————.

Answer 1

Answer:

parallelogram is a quadrilateral with two pairs of parallel sides. If we extend the sides of the parallelogram in both directions, we now have two parallel lines cut by two parallel transversals. The parallel line conjectures will help us to understand that the opposite angles in a parallelogram are equal in measure. When two parallel lines are cut by a transversal

Answer 2

Adjacent angles of a parallelogram are supplementary.

Let us consider Parallelogram PQRS.

To prove: ∠P + ∠Q = 180 degrees, ∠R + ∠S = 180 degrees

PQ ∥ RS and PS is a transversal.

As we know, the interior angles on the same side of a transversal are supplementary.

Therefore, ∠P + ∠S = 180°

Similarly, ∠Q + ∠R = 180°, ∠R + ∠S = 180° and ∠P + ∠Q = 180°.

Hence, the sum of any two adjacent angles of a parallelogram is equal to 180°.

Therefore, it is proved that any two adjacent or consecutive angles of a parallelogram are supplementary.

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