Question

1. in the diagram below, the lines are parallel. find all missing angles if the measure of angle 2 is 54°. 2) in the diagram below, the lines are parallel. find all missing angles if the measure of angle 5 is 104°. 04 hw - angles formed by parallel lines

Explanation:

Step1: Find angles related to angle 2 in problem 1

• Vertical angles: Vertical angles are equal. Since \(\angle2 = 54^{\circ}\), then \(\angle4=\angle2 = 54^{\circ}\) (vertical angles).
• Linear - pair angles: \(\angle1+\angle2 = 180^{\circ}\) (linear - pair of angles, supplementary). So \(\angle1=180^{\circ}-\angle2=180 - 54=126^{\circ}\). And \(\angle3=\angle1 = 126^{\circ}\) (vertical angles).
• Corresponding angles (for parallel lines \(m\) and \(n\)): \(\angle5=\angle1 = 126^{\circ}\) (corresponding angles). \(\angle7=\angle3 = 126^{\circ}\) (corresponding angles). \(\angle6=\angle2 = 54^{\circ}\) (corresponding angles). \(\angle8=\angle4 = 54^{\circ}\) (corresponding angles).

Step2: Find angles related to angle 5 in problem 2

• Linear - pair angles: \(\angle5+\angle6 = 180^{\circ}\) (linear - pair of angles, supplementary). Given \(\angle5 = 104^{\circ}\), then \(\angle6=180^{\circ}-\angle5=180 - 104 = 76^{\circ}\).
• Vertical angles: \(\angle7=\angle5 = 104^{\circ}\), \(\angle8=\angle6 = 76^{\circ}\).
• Corresponding angles (for parallel lines \(m\) and \(n\)): \(\angle1=\angle5 = 104^{\circ}\), \(\angle3=\angle7 = 104^{\circ}\), \(\angle2=\angle6 = 76^{\circ}\), \(\angle4=\angle8 = 76^{\circ}\).

Answer:

1. \(\angle1 = 126^{\circ}\), \(\angle3 = 126^{\circ}\), \(\angle4 = 54^{\circ}\), \(\angle5 = 126^{\circ}\), \(\angle6 = 54^{\circ}\), \(\angle7 = 126^{\circ}\), \(\angle8 = 54^{\circ}\)
2. \(\angle1 = 104^{\circ}\), \(\angle2 = 76^{\circ}\), \(\angle3 = 104^{\circ}\), \(\angle4 = 76^{\circ}\), \(\angle6 = 76^{\circ}\), \(\angle7 = 104^{\circ}\), \(\angle8 = 76^{\circ}\)