Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 16)°. Find the value of x and hence find the measure of each of its angles.
Let $A B C D$ be a parallelogram.
$L$ et $\angle A=(3 x-4)^{\circ}$
$\angle B=(3 x+16)^{\circ}$
$\therefore \angle A+\angle B=180^{\circ} \quad\left[\right.$ since the sum of adjacent angles of a parallelogram is $\left.180^{\circ}\right]$
$\Rightarrow 3 x-4+3 x+16=180$
$\Rightarrow 3 x-4+3 x+16=180$
$\Rightarrow 6 x+12=180$
$\Rightarrow 6 x=168$
$\Rightarrow x=\frac{168}{6}$
$\Rightarrow x=28$
$\therefore \angle A=(3 \times 28-4)^{\circ}$
$\quad=(84-4)^{\circ}$
$\quad=80^{\circ}$
$\angle B=((3 \times 28)+16)^{\circ}$
$\quad=(84+16)^{\circ}$
$\quad=100^{\circ}$
The opposite angles of a paralleleogram are equal.
$\therefore \angle C=\angle A=80^{\circ}$
$\angle D=\angle B=100^{\circ}$