1. **Stating the problem:** We have a circle with four inscribed angles measuring 80°, 32°, 25°, and three unknown angles labeled $a$, $b$, and $c$ opposite the known angles. We want to find the values of $a$, $b$, and $c$. 2. **Formula and rule:** The sum of all inscribed angles around a circle is 360° because they form a full circle. 3. **Set up the equation:** $$80 + 32 + 25 + a + b + c = 360$$ 4. **Simplify the known angles sum:** $$80 + 32 + 25 = 137$$ 5. **Rewrite the equation:** $$137 + a + b + c = 360$$ 6. **Isolate the unknown angles sum:** $$a + b + c = 360 - 137$$ $$a + b + c = 223$$ 7. **Conclusion:** The sum of the unknown angles $a$, $b$, and $c$ is 223°. Without additional information, we cannot find each angle individually. --- **Second problem (not solved as per instructions):** A circle with five inscribed angles including two labeled $c$ with 96°, and angles 50°, 40°, and unknown $y$. **Total distinct problems:** 2