1. **Problem statement:** We need to find the total length of the highway going around the bay, which consists of two segments: one 7 miles long at a 145° angle and another 2 miles long at a 140° angle. 2. **Understanding the problem:** The highway path is broken into two segments meeting at a point. The total length is the sum of these two segments. 3. **Formula used:** Since the problem asks for the length of the highway, and the segments are given, the total length $L$ is simply the sum: $$L = L_1 + L_2$$ where $L_1 = 7$ miles and $L_2 = 2$ miles. 4. **Calculation:** $$L = 7 + 2 = 9$$ 5. **Answer:** The length of the highway needed to go around the bay is $9$ miles. No rounding is needed since the sum is exact.