1. **Problem statement:** We have a transversal line $t$ crossing two parallel horizontal lines $a$ (upper) and $m$ (lower). Given angle 7 measures $113^\circ$, find the measurement of angle 6. 2. **Key properties:** When a transversal crosses parallel lines, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to $180^\circ$). 3. **Step 1:** Since lines $a$ and $m$ are parallel and $t$ is transversal, angles 6 and 7 are consecutive interior angles. 4. **Step 2:** Consecutive interior angles are supplementary, so: $$\text{angle }6 + \text{angle }7 = 180^\circ$$ 5. **Step 3:** Substitute the given value: $$\text{angle }6 + 113^\circ = 180^\circ$$ 6. **Step 4:** Solve for angle 6: $$\text{angle }6 = 180^\circ - 113^\circ$$ $$\text{angle }6 = 67^\circ$$ **Final answer:** The measurement of angle 6 is $67^\circ$.