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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 ∠A = (60 - x )° and∠C = (3x - 4).
We know that in a parallelogram, the opposite angles are equal.
Therefore,
∠A = ∠C
60 - x = 3x - 4
-x 3x = - 4 - 60
-4x = -64
x = 16
Thus, the given angles become
∠A = (60 - x)°
= (60 - 16)°
= 44 °
Similarly,
∠C = 44°
Also, adjacent angles in a parallelogram form the consecutive interior angles of parallel lines, which must be supplementary.
Therefore,
∠A +∠B = 180°
44° + ∠B = 180°
∠B = 180° - 44°
∠B = 136°
Similarly,
∠D = ∠B
∠D = 136°
Thus, the angles of a parallelogram are 44°,136°,44° and136° .
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