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Important Results Related to Parallelograms

If measures o...

Question

If measures opposite angles of a parallelogram are (60 − x)° and (3x − 4)°, then find the measures of angles of the parallelogram.

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Solution

Let ABCD be a parallelogram, with and .

We know that in a parallelogram, the opposite angles are equal.

Therefore,

Thus, the given angles become

Similarly,

Also, adjacent angles in a parallelogram form the consecutive interior angles of parallel lines, which must be supplementary.

Therefore,

Similarly,

Thus, the angles of a parallelogram are ,, and .

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Important Results Related to Parallelograms

Standard IX Mathematics

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