Question

Question 138
The adjacent angles of a parallelogram are $(2x-4{)}^{\circ }$ and $(3x-1{)}^{\circ }$. Find the measures of all angles of the parallelogram.

Answer 1

The adjacent angles of a parallelogram are supplementary.
$\therefore (2x-4{)}^{\circ }+(3x-1{)}^{\circ }={180}^{\circ }$
$\Rightarrow 5x-5^{\circ }={180}^{\circ }\Rightarrow 5x={185}^{\circ }\Rightarrow x=\frac{{185}^{\circ }}{5}\Rightarrow x={37}^{\circ }$

Thus, the adjacent angles are
$2x-4=2\times {37}^{\circ }-4=74-4={70}^{\circ }$.
and $3x-1=3\times {37}^{\circ }-1=111-1={110}^{\circ }$
Hence, the angles are ${70}^{\circ },{110}^{\circ },{70}^{\circ },{110}^{\circ }$.
[$\because$ Opposite angles in a parallelogram are equal].