Answers:
- d) vertical
- c) alternate interior
- f) supplementary
- e) alternate exterior
- g) corresponding
- e) alternate exterior
- f) supplementary
- c) alternate interior
- e) alternate exterior
Letters 'a', b, and h are never used.
Letters c and f show up twice each; e shows up 3 times.
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Explanations:
- Angles 1 and 2 are vertical angles because they are opposite one another in this X configuration. Vertical angles are always congruent.
- These angles are alternate interior angles because they are inside the parallel lines (hence the "interior") and they are on alternating sides of the transversal cut.
- The two angles shown here form a straight line, so that's what makes them supplementary. Supplementary angles add to 180 degrees.
- Angle 4 and angle 5 are on alternating sides of the transversal, but this time they are outside the parallel lines. So that's why we go for alternate exterior this time.
- Angles 5 and 6 are in the same southwest corner of each four-corner configuration, which makes them corresponding angles.
- It's the same idea as problem 4
- Same idea as problem 3.
- Same idea as problem 2.
- Same idea as problems 4 and 6.
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None of the angle pairs mentioned are consecutive interior angles. These types of angles are on the same side of the transversal, and inside the parallel lines. So we never use option 'a'. We cross off option h as well for pretty much identical reasoning. Options 'a' and h are the same thing, just slightly different wording.
We cross off option b as well because none of the angles add up to 90 degrees.
