Question

1. (2 - 107) examine the diagram at right. based on the information in the diagram, which angles can you determine? copy the diagram on your paper and find only those angles that you can justify.

Explanation:

Step1: Identify vertical - angle pairs

Vertical angles are equal. Given an angle of 106°, its vertical - angle is also 106°. Given an angle of 74°, its vertical - angle is 74°.

Step2: Identify supplementary - angle pairs

Supplementary angles add up to 180°. If an angle is 106°, its supplementary angle is 180 - 106=74°. If an angle is 74°, its supplementary angle is 180 - 74 = 106°.

Step3: Use parallel - line properties (if applicable)

Assuming the lines are parallel, corresponding angles are equal, alternate - interior angles are equal, and alternate - exterior angles are equal. But since no information about parallel lines is given, we rely only on vertical and supplementary angle relationships.

Answer:

All the angles in the diagram can be determined as 74° or 106° based on vertical - angle and supplementary - angle relationships. The angles are 74°, 106°, 74°, 106°, 74°, 106°, 74°, 106°.