Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of each angle of the parallelogram.
$O$ ppostie angles of a parallelogram are congurent.
$\therefore(3 x-2)^{\circ}=(50-x)^{\circ}$
$3 x^{\circ}-2^{\circ}=50^{\circ}-x^{\circ}$
$3 x^{\circ}+x^{\circ}=50^{\circ}+2^{\circ}$
$4 x^{\circ}=52^{\circ}$
$x^{\circ}=13^{\circ}$
Putting the value of $x$ in one angle :
$3 x^{\circ}-2^{\circ}=39^{\circ}-2^{\circ}$
$=37^{\circ}$
$O$ pposite angles are congurent:
$\therefore 50-x^{\circ}$
$=37^{\circ}$
Let the remaining two angles be $y$ and $z$.
Angles $y$ and $z$ are congurent because they are also opposite angles.
$\therefore y=z$
The sum of adjacent angles of a paralle $\log$ ram is equal to $180^{\circ}$.
$\therefore 37^{\circ}+y=180^{\circ}$
$y=180^{\circ}-37^{\circ}$
$y=143^{\circ}$
So, the anlges measure are :
$37^{\circ}, 37^{\circ}, 143^{\circ}$ and $143^{\circ}$