Here are the equations that both Elena and Diego wrote:

Question

Elena: "w" plus 148 equals 180

Diego: "x" plus 90 equals 148

1) What angle relationship did you need to recognize to use Elena’s equation?

2) What angle relationship did you need to recognize to use Diego’s equation?

Answer 1

1. To use Elena’s equation "w + 148 = 180," you would need to recognize that the angles are supplementary. This means that angle "w" and the angle measuring 148 degrees together add up to 180 degrees, which is the definition of supplementary angles.

2. To use Diego’s equation "x + 90 = 148," you would need to recognize that the angles are related as complements. In this case, angle "x" and the angle measuring 90 degrees together add up to 148 degrees, which indicates a situation involving complementary angles, although strictly speaking, complementary angles would sum to 90 degrees rather than just any number less than 180. Instead, Diego's equation may indicate that angle "x" is a part of a larger angle measure involving a combination of angles that sum to 148 degrees, but specifically, the equation hints at recognition of a missing angle in the context of a specific scenario (like adjacent angles).