1. **Problem:** Find the unknown angle at vertex R in parallelogram RQST where angle at S is 135°. 2. **Formula and rules:** In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180°). 3. Since angle S = 135°, angle R (adjacent to S) satisfies: $$\text{angle } R + \text{angle } S = 180^\circ$$ 4. Substitute the known value: $$\text{angle } R + 135^\circ = 180^\circ$$ 5. Solve for angle R: $$\text{angle } R = 180^\circ - 135^\circ = 45^\circ$$ 6. **Answer:** The measure of angle R is $45^\circ$. This uses the property that adjacent angles in a parallelogram are supplementary, which is key to solving angle problems in parallelograms.