Three angles of a quadrilateral ABCD are equal. Is it a parallelogram? Why or why not?

Solution:

Consider a parallelogram

Let ∠A = ∠B = ∠C = ∠D = 70º

As the sum of all the angles of a parallelogram is 360º

∠A + ∠B + ∠C + ∠D = 360º

Substituting the values

70º + 70º + 70º + ∠D = 360º

By further calculation

∠D = 360º - 210º

∠D = 150º

Here the opposite angles are not equal and the consecutive angles are not supplementary

Therefore, ABCD is not a parallelogram.

✦ Try This: Three angles of a quadrilateral PQRS are equal. Is it a parallelogram? Why or why not?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8

NCERT Exemplar Class 9 Maths Exercise 8.2 Sample Problem 3

Three angles of a quadrilateral ABCD are equal. Is it a parallelogram? Why or why not

Summary:

If three angles of a quadrilateral ABCD are equal it is not a parallelogram as the opposite angles are not equal

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