Question

5) The measure of two adjacent angle of a parallelogram are equal. Find the measure of each of the angle of the parallelogram​

Answer 1

Answer:

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-

Step-by-step explanation:

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