)) Two of the angles in a triangle measure \( 90^{\circ} \) and \( 75^{\circ} \). What is the measure of the third angle?

In a triangle, the sum of all three angles is always \( 180^{\circ} \). So, to find the measure of the third angle, you simply subtract the sum of the two known angles from \( 180^{\circ} \). In this case, it’s \( 180^{\circ} - (90^{\circ} + 75^{\circ}) = 180^{\circ} - 165^{\circ} = 15^{\circ} \). Therefore, the measure of the third angle is \( 15^{\circ} \). Did you know that triangles with a \( 90^{\circ} \) angle are called right triangles? They hold some fascinating properties, including the Pythagorean theorem, which relates the lengths of the sides. Right triangles are not just a staple in geometry classes; they also appear in real-world applications such as architecture and engineering. So, the next time you see a right triangle, think about all the incredible things that stem from it!