1. **Problem statement:** We have a transversal line $t$ crossing two parallel horizontal lines $a$ (upper) and $m$ (lower). The angles at the upper intersection are labeled 1, 2, 3, and 4, and at the lower intersection 5, 6, 7, and an implied angle. We are given that the angle below the lower line near the transversal is $113^\circ$. We need to find the measure of angle 3. 2. **Key concepts:** When a transversal crosses parallel lines, alternate interior angles are equal, corresponding angles are equal, and the sum of angles on a straight line is $180^\circ$. 3. **Step 1:** Identify the given angle. The $113^\circ$ angle is adjacent to angle 7 on the lower intersection. Since angles on a straight line sum to $180^\circ$, angle 7 is: $$\text{angle }7 = 180^\circ - 113^\circ = 67^\circ$$ 4. **Step 2:** Angles 3 and 7 are alternate interior angles formed by transversal $t$ crossing parallel lines $a$ and $m$. Therefore, they are equal: $$\text{angle }3 = \text{angle }7 = 67^\circ$$ 5. **Final answer:** The measure of angle 3 is $67^\circ$.