In parallelogram $PQRS$, the measure of angle $P$ is five times the measure of angle $Q$. What is the measure of angle $R$, in degrees?
I know that opposite angles in a parallelogram are equal, so angle $P$ and angle $R$ have the same measure, and angle $Q$ and angle $S$ have the same measure. I also know that the sum of the interior angles of any quadrilateral is $360$ degrees. Therefore, if I let $x$ be the measure of angle $Q$, I can write an equation for the sum of the angles as $5x + x + 5x + x = 360$. Simplifying this equation, I get $12x = 360$, so $x = 30$. This means that angle $Q$ and angle $S$ are both $30$ degrees, and angle $P$ and angle $R$ are both $5x = 5 \times 30 = 150$ degrees. 