Question

The adjacent angles of a parallelogram are in the ratio $2:1$. Find the measures of all the angles

Answer 1

Let the angles be $2x$ and $x$
∠A + ∠B = 2x + x = 180° (Adjacent angles of parallelograms are supplementary)
$2x+x=180°$
$3x=180°$
$x=180°/3=60°$
$\Rightarrow$ $\angle A=2x=60\times 2=120°$
$\Rightarrow$ $\angle B=60°$
$\Rightarrow$ $\angle C=\angle A=120°$ (Opposite angles of parallelogram)
$\angle D=\angle B=60°$ (Opposite angles of parallelogram)