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Question

The measure of the opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram.


Solution


For the given parallelogram ABCD,
mB = (3x – 2)°, m = (50 – x
(3x – 2)° =  (50 – x)°      (Opposite angles of a parallelogram are congruent)
4x = 52
x = 13
So, the measures of the different angles are
mD = (50 – x)° = (50 – 13)° = 37°
mB = 37°
mA +  mD = 180°                (Sum of adjacent angles of a parallelogram is 180°)
mA = 143°
mC = mA                            (Opposite angles of a parallelogram are congruent)
mA  = mC = 143°
mB  = mD= 37°

Mathematics
Mathematics(2013)
Standard VIII

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