Question

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

Explanation:

Step1: Recall property of parallelogram

In parallelogram \(PQRS\), \(\angle Q+\angle P = 180^{\circ}\) (adjacent - angles are supplementary). Also, \(\angle Q=(4a - 12)^{\circ}\), \(\angle P = 12a^{\circ}\), and \(\angle S=3a^{\circ}\). And \(\angle Q=\angle S\) (opposite - angles of a parallelogram are equal).

Step2: Set up equation for \(a\)

Since \(\angle Q=\angle S\), we have \(4a−12 = 3a\).
Solve for \(a\):
\[

$$\begin{align*} 4a-3a&=12\\ a&=12 \end{align*}$$

\]

Step3: Find \(\angle P\)

Substitute \(a = 12\) into the expression for \(\angle P\).
\(\angle P=12a^{\circ}\), so \(\angle P=12\times12^{\circ}=144^{\circ}\)

Answer:

\(144^{\circ}\)