1. **State the problem:** We need to approximate the measure of angle $\angle D$ in a right triangle with vertices $E$, $F$, and $D$, where $\angle F$ is the right angle. The sides given are $EF = 6.1$ and $ED = 6.7$. We will use the table of side length ratios for angles 55°, 65°, and 75° to find the closest match. 2. **Identify the sides relative to $\angle D$:** Since $\angle F$ is the right angle, $ED$ is the hypotenuse (opposite the right angle). The side $EF$ is adjacent to $\angle D$ because it connects vertices $E$ and $F$, and $F$ is the right angle vertex. 3. **Calculate the ratio of the adjacent leg to the hypotenuse:** $$\text{ratio} = \frac{EF}{ED} = \frac{6.1}{6.7} \approx 0.91$$ 4. **Compare with the table values for adjacent leg length / hypotenuse length:** - For 55°, ratio is 0.57 - For 65°, ratio is 0.42 - For 75°, ratio is 0.26 The calculated ratio 0.91 does not match these values, so check the other ratios. 5. **Calculate the ratio of the opposite leg to the hypotenuse:** The opposite leg to $\angle D$ is $FD$. We don't have $FD$ directly, but we can find it using the Pythagorean theorem: $$FD = \sqrt{ED^2 - EF^2} = \sqrt{6.7^2 - 6.1^2} = \sqrt{44.89 - 37.21} = \sqrt{7.68} \approx 2.77$$ 6. **Calculate the ratio of opposite leg to hypotenuse:** $$\frac{FD}{ED} = \frac{2.77}{6.7} \approx 0.41$$ 7. **Compare with the table values for opposite leg length / hypotenuse length:** - 55°: 0.82 - 65°: 0.91 - 75°: 0.97 Our ratio 0.41 is much smaller, so check the last ratio. 8. **Calculate the ratio of opposite leg to adjacent leg:** $$\frac{FD}{EF} = \frac{2.77}{6.1} \approx 0.45$$ 9. **Compare with the table values for opposite leg length / adjacent leg length:** - 55°: 1.43 - 65°: 2.14 - 75°: 3.73 Our ratio 0.45 is smaller than all these, so it seems the ratios do not match directly. 10. **Re-examine the problem:** The table's adjacent leg length / hypotenuse length values are: - 55°: 0.57 - 65°: 0.42 - 75°: 0.26 Our calculated ratio $\frac{EF}{ED} = 0.91$ is higher than all these, which suggests $EF$ is not the adjacent leg relative to $\angle D$. 11. **Try considering $EF$ as the opposite leg and $ED$ as hypotenuse:** $$\frac{EF}{ED} = 0.91$$ This matches the opposite leg length / hypotenuse length ratio for 65° (0.91) in the table. 12. **Conclusion:** The measure of $\angle D$ is approximately 65°. **Final answer: B 65°**