1. **State the problem:** We need to find the measure of angle $\angle MSP$ given two expressions for angles formed by a transversal intersecting two parallel lines. 2. **Given:** - $\angle MSP = (7x + 60)^\circ$ - $\angle QTS = (108 - 3x)^\circ$ 3. **Important rule:** When a transversal intersects two parallel lines, alternate interior angles are equal. 4. Since $\angle MSP$ and $\angle QTS$ are alternate interior angles, we set them equal: $$7x + 60 = 108 - 3x$$ 5. **Solve for $x$:** $$7x + 3x = 108 - 60$$ $$10x = 48$$ $$x = \frac{48}{10} = 4.8$$ 6. **Find $\angle MSP$ by substituting $x=4.8$ into $7x + 60$:** $$7(4.8) + 60 = 33.6 + 60 = 93.6^\circ$$ 7. **Answer:** The measure of $\angle MSP$ is $93.6^\circ$.