Looking at the worksheet, I need to identify angle relationships for each numbered item. Let me go through them one by one:
1. Angles 1 and 2 share a common side and vertex - they're adjacent
2. Angles 3 and 4 are opposite angles formed by intersecting lines - they're vertical
3. Angles 5 and 6 share a common side and vertex - they're adjacent
4. Angles 7 and 8 form a straight line together - they're a linear pair (which means they're also supplementary)
5. Angles 9 and 10 share a common side and vertex - they're adjacent
6. Angles 11 and 12 form a straight line together - they're a linear pair (supplementary)
7. Angles 13 and 14 are opposite angles formed by intersecting lines - they're vertical
8. The two angles add up to 90° (35° + 55° = 90°), so they're complementary. They also share a common side, making them adjacent too
9. The two angles add up to 180° (40° + 140° = 180°), so they're supplementary
10. Looking at the figure with point G as the center, acute vertical angles would be ∠1 & ∠5
11. Obtuse vertical angles would be ∠6 & ∠2
12. Adjacent angles sharing a common side would be ∠2 & ∠3
13. A linear pair forming a straight line would be ∠1 & ∠6
14. Complementary angles add to 90°, but none of these pairs do that
15. An angle supplementary to ∠FGE (∠6) would be another angle that forms a straight line with it - that's ∠6 itself since it's part of a linear pair
Final Answer:
1. Adjacent
2. Vertical
3. Adjacent
4. Linear pair / Supplementary
5. Adjacent
6. Linear pair / Supplementary
7. Vertical
8. Adjacent / Complementary
9. Supplementary
10. ∠1 & ∠5
11. ∠6 & ∠2
12. ∠2 & ∠3
13. ∠1 & ∠6
14. None
15. ∠6
Parent Tip: Review the logic above to help your child master the concept of pairs of angles worksheet.
