Question

The adjacent angle of a parallelogram are ${(2x+7)}^o$ and $(3x-2{)}^o$. Find all the angles.

Answer 1

The adjacent angles are given as ${\left(2x+7\right)}^{\circ }$ and ${\left(3x-2\right)}^{\circ }$.

Since, the sum of the adjacent angles of a parallelogram is ${180}^{\circ }$, then,

$2x+7+3x-2=180$

$5x+5=180$

$5x=175$

$x=35$

${\left(2x+7\right)}^{\circ }={\left(2\left(35\right)+7\right)}^{\circ }$

$={77}^{\circ }$

${\left(3x-2\right)}^{\circ }={\left(3\left(35\right)-2\right)}^{\circ }$

$={103}^{\circ }$

And since the opposite angles of a parallelogram is equal, so, the angles will be ${77}^{\circ },{103}^{\circ },{77}^{\circ },{103}^{\circ }$.