Two adjacent angles of a parallelogram are in the ratio $1:2$. Find the angles.

In the adjacent figure, $\mathrm{PQRS}$ is a parallelogram. Find each angle of the parallelogram marked with a letter.

In the adjacent figure, $\mathrm{ABCD}$ is a parallelogram and AC is its diagonal. Prove that $△\mathrm{BCA}\cong △\mathrm{DAC}$. Hence, prove that $\mathrm{BC}=\mathrm{DA}$

In the adjacent figure, $\mathrm{ABCD}$ is a parallelogram and AC is its diagonal. Prove that $△\mathrm{BCA}\cong △\mathrm{DAC}$. Hence prove that, $\mathrm{AB}=\mathrm{CD}$

In the adjacent figure, $\mathrm{ABCD}$ is a parallelogram and AC is its diagonal. Prove that $△\mathrm{BCA}\cong △\mathrm{DAC}$. Hence prove that,$\angle \mathrm{B}=\angle \mathrm{D}$