1. **Problem:** Find the length of the angle indicated for trapezoid 1, where angle at S is 65° and angle at R is unknown. 2. **Formula and rules:** In a trapezoid, consecutive angles between the parallel sides are supplementary, meaning their measures add up to 180°. 3. **Step:** Since angles S and R are consecutive angles along one leg, we use: $$\text{angle } S + \text{angle } R = 180^\circ$$ 4. **Substitute known value:** $$65^\circ + \text{angle } R = 180^\circ$$ 5. **Solve for angle R:** $$\text{angle } R = 180^\circ - 65^\circ = 115^\circ$$ 6. **Answer:** The angle at vertex R is $115^\circ$.