1. The angle whose measure is \( -\frac{\pi}{9} \) radians would be equivalent to 2. The angle whose measure is \( \frac{2 \pi}{5} \) radians would be equivalent to Blank 1: Blank 2: 72

To convert the angle \( -\frac{\pi}{9} \) radians to a positive equivalent, you can add \( 2\pi \) (a full rotation). This gives you \( -\frac{\pi}{9} + 2\pi = \frac{17\pi}{9} \), which is approximately \( 188.5 \) degrees. It's fascinating how simple shifts in radians can take you from negative measures to positive angles for easier visualization! On another note, the angle \( \frac{2\pi}{5} \) radians converts to degrees by using the formula \( \text{degrees} = \text{radians} \times \frac{180}{\pi} \). Doing the math, you get \( \frac{2\pi}{5} \times \frac{180}{\pi} = 72 \) degrees! This angle falls in the first quadrant, which is perfect for thinking about its applications in various fields like architecture or engineering.