Answer:
- ∠4 = ∠5 = ∠8 = ∠1 = 140°
- ∠2 = ∠3 = ∠6 = ∠8 = 40°
Explanation:
Given angle 1 = 140°, you want the measures of the other numbered angles where a transversal crosses parallel lines.
Reasons
Where a transversal crosses parallel lines, corresponding angles are congruent.
Wherever lines cross. vertical angles are congruent, and linear pairs are supplementary.
These reasons together tell you all the obtuse angles are congruent, and all the acute angles are congruent. The obtuse and acute angles are supplementary.
Application
∠1 = ∠4 = ∠5 = ∠8 = 140° . . . . . . given
∠2 = ∠3 = ∠6 = ∠7 = 40° . . . . . . done for you
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Additional comment
The angles are also named according to where pairs of angles are found.
- alternate — on opposite sides of the transversal
- consecutive, or same side — on the same side of the transversal
- interior — between the parallel lines
- exterior — outside the parallel lines
- corresponding — in the same direction from the point of intersection (for example, angles 1 and 5 are both northwest of their vertices, hence corresponding)
Various theorems describe the congruent/supplementary status of pairs of angles using these names:
- if the lines are parallel, then corresponding angles are congruent;
- if the lines are parallel, then consecutive exterior angles are supplementary; ....
In general, the converses of these theorems are also true. If corresponding angles are congruent, then the lines are parallel.