\( \begin{array}{l}\begin{array}{l}\text { A student is trying to construct triangles using four different sets of angles. The angles in each set are } \\ \text { below. Which set will form a triangle? }\end{array} \\ 90^{\circ}, 90^{\circ}, 90^{\circ} \\ 45^{\circ}, 65^{\circ}, 70^{\circ} \\ 50^{\circ}, 50^{\circ}, 50^{\circ}\end{array} 150^{\circ}, 110^{\circ}, 10 \)

To determine which set of angles can form a triangle, we must remember that the sum of the interior angles in a triangle always equals \(180^\circ\). Checking each set: 1. \(90^\circ + 90^\circ + 90^\circ = 270^\circ\) – can't be a triangle. 2. \(45^\circ + 65^\circ + 70^\circ = 180^\circ\) – this is a valid triangle! 3. \(50^\circ + 50^\circ + 50^\circ = 150^\circ\) – can't be a triangle. 4. \(150^\circ + 110^\circ + 10^\circ = 270^\circ\) – can't be a triangle. So the set that will form a triangle is \(45^\circ, 65^\circ, 70^\circ\)! If you're anything like me, you might have at least once tried to use strange angle combinations to create a triangle, only to find out they didn’t work! It’s a great little reminder that angles are like ingredients; putting in the right mix is critical. So, next time you're feeling experimental with shapes, just remember: keep it under 180°! On the flip side, this exercise is fantastic for learning geometry! If triangles interest you, consider diving deeper into the world of Euclidean geometry. You can explore not just triangles, but also polygons and the rich relationships they have with angles and sides. There are numerous engaging resources, from textbooks to online courses, that will elevate your understanding of these shapes to remarkable levels!