Question

If measures opposite angles of a parallelogram are $(60-x{)}^{\circ }and(3x-4{)}^{\circ },$ then find the measures of angles of the parallelogram.

Answer 1

Opposite angles of a ||gm ABCD are $(60-x{)}^{\circ }and(3x-4{)}^{\circ },$

But opposite angles of a ||gm are equal , the

${60}^{\circ }-x^{\circ }=3x-4^{\circ }\Rightarrow {60}^{\circ }+4^{\circ }=3x+x\Rightarrow 4x={64}^{\circ }\Rightarrow x=\frac{{64}^{\circ }}{4^{\circ }}={16}^{\circ }\therefore \angle A={60}^{\circ }-x={60}^{\circ }-{16}^{\circ }={44}^{\circ }But\angle A+\angle B={180}^{\circ }$ (Sum of consecutive angle)

$\Rightarrow {44}^{\circ }+\angle B={180}^{\circ }\Rightarrow \angle B={180}^{\circ }-{44}^{\circ }\Rightarrow \angle B={136}^{\circ }But\angle A=\angle Cand\angle B=\angle D$ (Opposite angles)

$\therefore Anglesare{44}^{\circ },{136}^{\circ },{44}^{\circ },{136}^{\circ }$