Question

use the following images of angles to name angles that fit the definitions for the following:

1. vertical angles _______________
2. adjacent angles _______________
3. corresponding angles _______________
4. linear pair _______________
5. right angle _______________
6. complementary angles _______________
7. supplementary angles _______________
8. alternate interior angles _______________
9. alternate exterior angles _______________
10. same-side interior angles _______________
11. same-side exterior angles _______________
12. congruent angles _______________

Explanation:

1. Vertical angles: Pairs of opposite angles formed by intersecting lines, congruent.
2. Adjacent angles: Share a vertex and side, no overlapping interior.
3. Corresponding angles: Lie in same position relative to parallel lines/transversal, congruent.
4. Linear pair: Adjacent angles forming a straight line, sum to 180°.
5. Right angle: Measures exactly 90°.
6. Complementary angles: Two angles summing to 90°.
7. Supplementary angles: Two angles summing to 180°.
8. Alternate interior angles: Lie between parallel lines, opposite sides of transversal, congruent.
9. Alternate exterior angles: Lie outside parallel lines, opposite sides of transversal, congruent.
10. Same-side interior angles: Lie between parallel lines, same side of transversal, supplementary.
11. Same-side exterior angles: Lie outside parallel lines, same side of transversal, supplementary.
12. Congruent angles: Have equal measure (any matching angle pair).

Answer:

1. Vertical angles: $\angle AEC$ and $\angle BED$
2. Adjacent angles: $\angle 1$ and $\angle 2$
3. Corresponding angles: $\angle 1$ and $\angle 6$
4. Linear pair: $\angle LMP$ and $\angle PMN$
5. Right angle: $\angle AOB$
6. Complementary angles: $\angle AOF$ and $\angle FOB$
7. Supplementary angles: $\angle LMP$ and $\angle PMN$
8. Alternate interior angles: $\angle 3$ and $\angle 6$
9. Alternate exterior angles: $\angle 2$ and $\angle 7$
10. Same-side interior angles: $\angle 3$ and $\angle 5$
11. Same-side exterior angles: $\angle 1$ and $\angle 7$
12. Congruent angles: $\angle AEC$ and $\angle BED$