Two of the angles in a triangle measure \( 30^{\circ} \) and \( 134^{\circ} \). 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 interior angles in a triangle is always \( 180^{\circ} \). First, add the measures of the two known angles: \( 30^{\circ} + 134^{\circ} = 164^{\circ} \). Then, subtract this sum from \( 180^{\circ} \): \( 180^{\circ} - 164^{\circ} = 16^{\circ} \). Therefore, the measure of the third angle is \( 16^{\circ} \). Triangles have been a fundamental shape in mathematics and have historical significance dating back to ancient civilizations. For instance, the Egyptians were known to use right triangles in construction, such as the pyramids, cleverly applying the properties of the \( 3-4-5 \) triangle to create right angles through their building methods. In real-world applications, understanding the angles in triangles is crucial in various fields such as architecture, engineering, and navigation. For instance, architects use these principles to design stable structures and ensure that angles are correctly calculated to achieve both aesthetics and strength in their buildings.