Question

Two opposite angles of a parallelogram are $(3x-2{)}^{\circ }and(50-x{)}^{\circ }.$ Find the measure of each angle of the parallelogram.

Answer 1

$\because$ Opposite angles of a parallelogram are equal

$\therefore 3x-2=50-x$

$\Rightarrow 3x+x=50+2\Rightarrow 4x=52\Rightarrow x=\frac{52}{4}=13\therefore \angle A=3x-2=3\times 13-2={39}^{\circ }-2={37}^{\circ }\angle C={50}^{\circ }-x={50}^{\circ }-13={37}^{\circ }But\angle A+\angle B={180}^{\circ }\therefore {37}^{\circ }+\angle B={180}^{\circ }\Rightarrow \angle B={180}^{\circ }-{37}^{\circ }={143}^{\circ }$

and $\angle D=\angle B$ (Opposite angles of a ||gm)

$\therefore \angle D={143}^{\circ }$

Hence angles and ${37}^{\circ },{143}^{\circ },{37}^{\circ },{143}^{\circ }$