Angle Relations
1. The problem asks for the order and relation between pairs of angles based on the graph and given angle measures.
2. From the figure with angles 90° and 68° and the labeled angles 1 to 6, we can deduce angle relationships.
3. Since the figure includes angles at intersections and vertices, vertical angles are equal, corresponding angles or angles on a straight line sum to 180°.
4. Evaluate each pair:
- ∠1 and ∠4: If ∠1 and ∠4 are vertical angles, then $m\angle1 = m\angle4$.
- ∠3 and ∠6: If they are also vertical or corresponding, then $m\angle3 = m\angle6$.
- ∠4 and ∠2: From the 90° and 68° marks and their positions, we infer $m\angle4 < m\angle2$.
- ∠1 and ∠5: Based on the diagram, $m\angle1 > m\angle5$.
- ∠6 and ∠2: Given the 90° and 68° angles and their relation, $m\angle6 < m\angle2$.
5. Check inequalities:
- 1. $m\angle1 > m\angle5$ : TRUE
- 2. $m\angle3 < m\angle2$ : TRUE
- 3. $m\angle4 > m\angle6$ : FALSE, because $m\angle4 = m\angle1 = m\angle6$ or similar equality or less.
- 4. $m\angle1 > m\angle4$ : FALSE, vertical angles equal
- 5. $m\angle5 < m\angle3$ : TRUE
- 6. $m\angle6 < m\angle2$ : TRUE
Final answers:
C. Relations:
- ∠1 = ∠4
- ∠3 = ∠6
- ∠4 < ∠2
- ∠1 > ∠5
- ∠6 < ∠2
D. Inequalities:
- 1. TRUE
- 2. TRUE
- 3. FALSE
- 4. FALSE
- 5. TRUE
- 6. TRUE