Question

The adjacent angles of a parallelogram are in the ratio $2:3$. Find the measure of all its angles.

Answer 1

The measures of the adjacent angles of a parallelogram add up to be ${180}^{\circ }$, or they are supplementary.

Hence, the angles are $\angle 1=2x$ and $\angle 2=3x$

$\angle 1$$+\angle 2$$={180}^{\circ }$

$2x+3x={180}^{\circ }$

$x={36}^{\circ }$

$\angle 1=\angle 3=2x={72}^{\circ }.$

$\angle 2=\angle 4=3x={108}^{\circ }.$