Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°.
Hence, it is proved that any two adjacent or consecutive angles of a parallelogram are supplementary.
If one angle is a right angle, then all four angles are right angles:
From the above theorem, it can be decided that if one angle of a parallelogram is a right angle (that is equal to 90 degrees), then all four angles are right angles. Hence, it will become a rectangle.
Since the adjacent sides are supplementary.
For example, ∠A, ∠B are adjacent angles and ∠A = 90°, then:
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Answer:
We know that interior angles on the same side of a transversal are supplementary.
Therefore, ∠A + ∠D = 180°
Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°.
Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°.
Hence, it is proved that any two adjacent or consecutive angles of a parallelogram are supplementary.
If one angle is a right angle, then all four angles are right angles:
From the above theorem, it can be decided that if one angle of a parallelogram is a right angle (that is equal to 90 degrees), then all four angles are right angles. Hence, it will become a rectangle.
Since the adjacent sides are supplementary.
For example, ∠A, ∠B are adjacent angles and ∠A = 90°, then:
∠A + ∠B = 180°
90° + ∠B = 180°
∠B = 180° – 90°
∠B = 90°
Similarly, ∠C = ∠D = 90°
Step-by-step explanation: