48. Yes, the classmate is correct. The complements of congruent angles are congruent.
49. This is one of those questions that ask you to notice something—without telling you what. There's a lot of that in modern math texts, as they are attempting to get you to discover the rules of math on your own.
a) For this purpose, it seems these expressions will be adequate:
... ∠BAE + ∠DAE = ∠BAD = 180°
... ∠BAE + ∠CAB = ∠CAE = 180°
b) If you subtract ∠BAE from both equations, you get
... ∠DAE = 180° - ∠BAE = ∠CAB
This tells you angle supplementary to the same angle are congruent.
Vertical angles are congruent.
50.
a) Substituting the required variables in the given relations, you have ...
... y₁ = 90° - x
... y₂ = 180° - x
b) See the attachment.
- The domain and range of the function involving y₁ is 90°.
- The domain and range of the function involving y₂ is 180°.
