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

#### Solution

\[\text{ Oppostie angles of a parallelogram are congurent } . \]

\[ \therefore \left( 3x - 2 \right)° = \left( 50 - x \right)°\]

\[3x°- 2° = 50°- x°\]

\[3x°+ x°= 50° + 2°\]

\[4x°= 52°\]

\[x° = 13°\]

\[\text{ Putting the value of x in one angle }: \]

\[3x° - 2°= 39°- 2°\]

\[ = 37°\]

\[\text{ Opposite angles are congurent }: \]

\[ \therefore 50 - x°\]

\[ = 37°\]

\[\text{ Let the remaining two angles be y and z } . \]

\[\text{ Angles y and z are congurent because they are also opposite angles } . \]

\[ \therefore y = z\]

\[\text{ The sum of adjacent angles of a paralle\logram is equal to } 180° . \]

\[ \therefore 37°+ y = 180°\]

\[y = 180°- 37°\]

\[y = 143°\]

\[\text{ So, the anlges measure are }: \]

\[37°, 37°, 143° \text{ and } 143°\]