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Answer:

Hint – Let ABCD be a parallelogram with ∠A=∠B. Use the concept that the sum of adjacent angles is equal to 180 degrees.

Complete step-by-step solution -

Refer to the figure below of parallelogram ABCD-

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We have been given in the question that adjacent angles of a parallelogram are equal.

To find: Measure of each angle of the parallelogram.

Let ABCD be a parallelogram with ∠A=∠B.

Now, we know that: Sum of adjacent angles =180∘.

∠A+∠B=180∘

Putting ∠A=∠B in the above equation, we get-

∠A+∠A=180∘⇒2∠A=180∘⇒∠A=∠B=90∘

Now, we know the opposite angles of a parallelogram are equal.

Therefore, ∠C=∠A=90∘(Opposite angles)

And also, ∠D=∠B=90∘(Opposite angles)

Thus, each angle of the parallelogram measures 90∘.

Thus, the parallelogram with each angle 90 degrees is shown below-

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Note – Whenever such types of question appear, assume a parallelogram and then use the conditions given in the question. As mentioned in the solution, the adjacent angles are equal, i.e., ∠A=∠B, so using the concept that the sum of adjacent angles is equal to 180 degrees, find the angles A and B, and then C and D angles can be found out by the property that opposite angles of parallelogram are equal.

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Answer:

You can add hence proved at the last .

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