9514 1404 393
Answer:
see attached
Step-by-step explanation:
When a transversal line crosses parallel lines, it creates 8 angles. If the transversal crosses at right angles, every one of those angles is a right angle.
If the transversal does not cross at right angles, it creates 4 acute angles and 4 obtuse angles. The acute and obtuse angles are supplementary to each other, since they form linear pairs.
All of the acute angles are congruent, as are all of the obtuse angles. [this is the simplicity of it — only true if the lines are parallel]
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Different pairs of angles have names. Angles on opposite sides of a point of intersection are "vertical" angles. Angles between the parallel lines are "interior" angles, and those outside are "exterior" angles. Angles on the same side of the transversal are called "same-side" or "consecutive" angles. Angles on opposite sides of the transversal are called "alternate" angles.
Angles in the same direction from the points of intersection (upper-left, for example) are called "corresponding" angles.
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Angle relationships are often described in the terms described above. For example, every pair of "corresponding angles" is congruent, as are "alternate interior" or "alternate exterior" angles. In any geometry (not just one like this), "vertical angles" are congruent.
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You are given the measure of angle 4 (122°). This tells you every obtuse angle in the figure is 122°, and every acute angle in the figure is 180°-122° = 58°. All you need to do to find the angle measures is identify the angle as acute or obtuse.
For justification, you may be expected to determine the relationship of the requested angle to angle 4.
7. ∠8 — part of linear pair; supplementary to ∠4
8. ∠5 — alternate exterior; congruent to ∠4
9. ∠2 — corresponding; congruent to ∠4
10. ∠1 — consecutive exterior; supplementary to ∠4
11. ∠6 — vertical to ∠1*, so the same measure as ∠1
12. ∠7 — vertical to ∠4; congruent to ∠4
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* angles 1 and 4 have no named relationship. angle 2 is corresponding to angle 4, and angle 5 is alternate exterior with respect to angle 4. Each of those is supplementary to angle 6, so angle 6 is supplementary to angle 4.
