Answer:
- Complementary: D, F
- Supplementary: A, C
- Neither: B, E
Step-by-step explanation:
A: We see angles 1 and 2 are both on the line - they make up the line. A line is 180 degrees, so we know that ∠1 + ∠2 = 180°. By definition of supplementary angles (angles that add up to 180), ∠1 and ∠2 are supplementary.
B: Let's add up 64.5 to 26.5:
64.5 + 26.5 = 91
Since ∠1 and ∠2 don't add up to 90, by definition of complementary angles (angles that add up to 90), then ∠1 and ∠2 are not complementary. So B is neither.
C: Here, ∠2 and ∠3 lie on a line, whose degree measure is always 180 degrees. Thus, these are supplementary.
D: The little square that makes up angles 2 and 3 indicates a 90-degree angle. That means ∠2 + ∠3 = 90, so they're complementary.
E: If we add these two angles together, we get: 132 + 38 = 170°. Clearly, this is not 90 or 180, so this is neither.
F: Angles 1, 2, and 3 all lie on a line, which means that they add up to 180. We also see that ∠2 = 90. So we have:
∠1 + ∠2 + ∠3 = 180
∠1 + 90 + ∠3 = 180
∠1 + ∠3 = 180 - 90 = 90
Thus, angles 1 and 3 are complementary.
The answer is:
- Complementary: D, F
- Supplementary: A, C
- Neither: B, E
