Question

1. look at the figure, ▱pqrs. find m∠p.

Explanation:

Step1: Recall property of parallelogram

In parallelogram $PQRS$, opposite - angles are equal and adjacent - angles are supplementary. $\angle Q$ and $\angle P$ are adjacent angles, so $\angle Q+\angle P = 180^{\circ}$.

Step2: Calculate $\angle Q$

First, simplify the measure of $\angle Q$. Given $\angle Q=(4x - 12)^{\circ}$. We are not given the value of $x$, but we can also use the fact that in a parallelogram, the sum of adjacent angles is $180^{\circ}$. Let's assume we use the angle - sum property directly. We know that one of the adjacent - angle relationships. If we consider the fact that the sum of adjacent angles in a parallelogram is $180^{\circ}$. Let's assume we know that the other adjacent angle information is not relevant for the direct calculation. Since $\angle Q$ and $\angle P$ are adjacent, and we know that the sum of adjacent angles in a parallelogram is $180^{\circ}$. If we assume the given angle $\angle S = 36^{\circ}$, then $\angle Q=36^{\circ}$ (opposite angles of a parallelogram are equal). Then $\angle P=180^{\circ}-\angle Q$.

Step3: Substitute the value of $\angle Q$

Substitute $\angle Q = 36^{\circ}$ into the formula $\angle P=180^{\circ}-\angle Q$. So, $\angle P=180 - 36=144^{\circ}$.

Answer:

$144^{\circ}$