Let’s go through each problem one by one. We’ll identify the angle pair, decide if they’re congruent or supplementary, and then find the missing angle.
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Problem 1)
Angle given: 68°
Looking at the diagram, both angles are in matching positions on the same side of the transversal — that’s
corresponding angles.
Corresponding angles are
congruent when lines are parallel.
So, x = 68°
✔ Check: Yes, corresponding → congruent → x = 68°
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Problem 2)
Angle given: 134°
These two angles are on the same side of the transversal and between the parallel lines — that’s
same-side interior.
Same-side interior angles are
supplementary (add to 180°).
So, x + 134 = 180 → x = 180 - 134 = 46°
✔ Check: 46 + 134 = 180 → correct.
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Problem 3)
Angle given: 120°
These angles are opposite each other where two lines cross — that’s
vertical angles.
Vertical angles are always
congruent.
So, x = 120°
✔ Check: Vertical angles are equal → x = 120°
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Problem 4)
Angle given: 101°
These angles are on opposite sides of the transversal and inside the parallel lines — that’s
alternate interior.
Alternate interior angles are
congruent.
So, x = 101°
✔ Check: Alternate interior → congruent → x = 101°
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Problem 5)
Angle given: 77°
These angles are on the same side of the transversal but outside the parallel lines — that’s
same-side exterior.
Same-side exterior angles are
supplementary.
So, x + 77 = 180 → x = 180 - 77 = 103°
✔ Check: 103 + 77 = 180 → correct.
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Problem 6)
Angle given: 106°
These angles are on opposite sides of the transversal and inside the parallel lines — that’s
alternate interior.
Alternate interior angles are
congruent.
So, x = 106°
✔ Check: Alternate interior → congruent → x = 106°
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Problem 7)
Angle given: 74°
These angles are on the same side of the transversal and between the parallel lines — that’s
same-side interior.
Same-side interior angles are
supplementary.
So, x + 74 = 180 → x = 180 - 74 = 106°
✔ Check: 106 + 74 = 180 → correct.
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Problem 8)
Angle given: 142°
These angles are on opposite sides of the transversal and outside the parallel lines — that’s
alternate exterior.
Alternate exterior angles are
congruent.
So, x = 142°
✔ Check: Alternate exterior → congruent → x = 142°
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Final Answer:
1) Corresponding, Congruent, x = 68°
2) Same-Side Interior, Supplementary, x = 46°
3) Vertical, Congruent, x = 120°
4) Alternate Interior, Congruent, x = 101°
5) Same-Side Exterior, Supplementary, x = 103°
6) Alternate Interior, Congruent, x = 106°
7) Same-Side Interior, Supplementary, x = 106°
8) Alternate Exterior, Congruent, x = 142°
Parent Tip: Review the logic above to help your child master the concept of finding angle measures parallel lines cut transversal worksheet.
