Properties of a Parallelogram

The adjacent angles of a trapezium $ABCD$, in which $AB\parallel CD$, are $2x+50$ and $2x-10$. Find the measures of the angles.

In the following figure, $ABCD$ is a parallelogram with diagonal $AC$. If $DM$ and $BN$ are drawn perpendiculars to $AC$, then find the values of $x, y$ and $z$.

The opposite angles of a parallelogram are $\left(4y+5\right)°$ and $\left(3y+15\right)°$. Find all the angles of the parallelogram.

In the following figure, $PQRS$ is a parallelogram. Find the measures of $\angle SPR$ and $\angle PQR$.

The adjacent angles of a parallelogram are in the ratio $2:7$. Find the measure of each angle.

One of the adjacent angles of a parallelogram is half the other angle. Find all the angles of the parallelogram.

In the following figure, $PQRS$ is an isosceles trapezium with $PQ\parallel RS$. Find the measure of side $PQ$.

In the following figure, $PQRS$ is a trapezium with $PQ\parallel RS$. The bisectors of $\angle P$ and $\angle Q$ meet at $M$ on side $RS$ such that $\angle PMQ = 80°$. If $PM = QM$, then show that $\angle S+\angle R=160°$.

One angle of a parallelogram can be found by multiplying the other by two and subtracting $30$ from the product. Find each angle of the parallelogram.

One of the adjacent angles of a parallelogram is $20°$ more than the other. Find all the angles of the parallelogram.

In a parallelogram, one of the angle is $55°$. Find the measure of each angle.

What is a parallelogram with all four sides equal?

One of the exterior and the interior angles of a parallelogram are in the ratio $2:3$. Find all the angles of the parallelogram.

In the given figure, $PQRS$ is a parallelogram. Find the value of $\angle x, \angle y,$ and $\angle z$.

One angle of the adjacent angles of a parallelogram is $\frac{4}{5}\mathrm{th}$ of the other. Find each of the angles of the parallelogram.

In the given figure, $ABCD$ is a parallelogram with $\angle A=70°$. The bisectors of $\angle B$ and $\angle C$ meet at $P$ inside the parallelogram. Find the measure of $\angle BPC$.

In the given figure, $PQRS$ is a parallelogram with $\angle SPQ=80°$ and $\angle SQR=45°$. Find the measure of $\angle RSQ$ and $\angle PSQ$.

The adjacent angles of a parallelogram are $\left(3x+8\right)°$ and $\left(10-x\right)°$. Find the measure of $x$.

The sum of the opposite angles of parallelogram is $156°$. Find the remaining angles.

One of the angles of a parallelogram is $150°$. Find the remaining angles.