1. **State the problem:** We have a triangle with a height of $1 \frac{5}{8}$ inches (which is $1.625$ inches), a base length of $4 \frac{1}{2}$ inches (which is $4.5$ inches), and one angle given as $40^\circ$. We need to find the missing angle at the base adjacent to the $4.5$ inch side. 2. **Convert mixed numbers to decimals:** - Height $= 1 \frac{5}{8} = 1 + \frac{5}{8} = 1 + 0.625 = 1.625$ inches - Base $= 4 \frac{1}{2} = 4 + \frac{1}{2} = 4 + 0.5 = 4.5$ inches 3. **Identify the triangle type and known angles:** - The triangle has a right angle at the height (since height is perpendicular to the base). - One angle is $40^\circ$. - The missing angle is at the base adjacent to the $4.5$ inch side. 4. **Use the triangle angle sum rule:** The sum of angles in any triangle is $180^\circ$. 5. **Calculate the missing angle:** Let the missing angle be $x$. Since one angle is $90^\circ$ (right angle), and another is $40^\circ$, then: $$x = 180^\circ - 90^\circ - 40^\circ = 50^\circ$$ 6. **Answer:** The missing angle is $50^\circ$.