1. **State the problem:** Determine if a spherical triangle can be constructed with sides $a=170^\circ$, $b=100^\circ$, and $c=80^\circ$. 2. **Recall the spherical triangle inequality:** For any spherical triangle with sides $a$, $b$, and $c$ (measured as angles in degrees), the sum of any two sides must be greater than the third side, and the sum of all three sides must be less than $360^\circ$. 3. **Check the inequalities:** - $a + b = 170^\circ + 100^\circ = 270^\circ > c = 80^\circ$ (valid) - $b + c = 100^\circ + 80^\circ = 180^\circ > a = 170^\circ$ (valid) - $a + c = 170^\circ + 80^\circ = 250^\circ > b = 100^\circ$ (valid) 4. **Check the sum of all sides:** $$a + b + c = 170^\circ + 100^\circ + 80^\circ = 350^\circ < 360^\circ$$ 5. **Conclusion:** Since all pairwise sums are greater than the third side and the total sum is less than $360^\circ$, it is possible to construct such a spherical triangle. **Final answer:** Yes, it is possible to construct the spherical triangle with the given sides.