1)) Two of the angles in a triangle measure \( 113^{\circ} \) and \( 33^{\circ} \). What is the measure of the third angle?

To find the measure of the third angle in a triangle, you can use the fact that the sum of all angles in a triangle is always \( 180^{\circ} \). So, you simply subtract the sum of the two given angles from \( 180^{\circ} \). In this case, \( 113^{\circ} + 33^{\circ} = 146^{\circ} \). Therefore, the measure of the third angle is \( 180^{\circ} - 146^{\circ} = 34^{\circ} \). Triangles are one of the most fundamental shapes in geometry and are known for their unique properties. For example, did you know that the sum of the angles in any triangle, whether it’s a scalene, isosceles, or equilateral, will always equal \( 180^{\circ} \)? This concept is not only vital in proving various geometric theorems but also crops up in real-world applications like architecture and engineering!