1. **State the problem:** We are given two angles at point P, $m\angle 1 = (x + 28)^\circ$ and $m\angle 2 = (3x + 14)^\circ$, with lines $MN \parallel PQ$ and $NP$ a transversal. We want to find $x$ and answer if a line perpendicular to one of two parallel lines is also perpendicular to the other. 2. **Use angle relationships:** Since $MN \parallel PQ$ and $NP$ is a transversal, angles $\angle 1$ and $\angle 2$ are consecutive interior angles, which are supplementary. This means: $$m\angle 1 + m\angle 2 = 180^\circ$$ 3. **Set up the equation:** $$ (x + 28) + (3x + 14) = 180 $$ 4. **Simplify:** $$ x + 28 + 3x + 14 = 180 $$ $$ 4x + 42 = 180 $$ 5. **Isolate $x$:** $$ 4x = 180 - 42 $$ $$ 4x = 138 $$ 6. **Divide both sides by 4:** $$ x = \frac{138}{4} $$ $$ x = \cancel{\frac{138}{\cancel{4}}} \text{ but we show cancellation as } x = \frac{\cancel{138}}{\cancel{4}} \text{ is incorrect, so just } x = \frac{138}{4} = 34.5 $$ 7. **Answer the question about perpendicular lines:** If a line is perpendicular to one of two parallel lines, it is also perpendicular to the other. This is because parallel lines have the same direction, so a line forming a right angle with one must form a right angle with the other. **Final answers:** - $x = 34.5$ - Yes, a line perpendicular to one parallel line is perpendicular to the other.