Subjects geometry

Angle Relations

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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