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Answer:
- Angles 4, 5, 6, 7, 8, 9 are 82°
- Angles 1, 2, 3, 10, 11, 12 are 98°
Step-by-step explanation:
Angles are related in this geometry by being either congruent or supplementary. Corresponding and vertical angles are congruent; any linear pair of angles is supplementary.
The given angle 5 is on the southwest corner of the intersection of the parallel line with the transversal. All southwest and northeast angles are congruent to that. That is, angles 4, 5, 6, 7, 8, 9 will all have the same measure. The remaining angles will have the supplementary measure.
Angles 4, 5, 6, 7, 8, 9 are 82°
Angles 1, 2, 3, 10, 11, 12 are 98°
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As you know, supplementary angles total 180°, so each is found by subtracting the other from 180°: 180° -82° = 98°.
