Angle Pairs Created By Parallel Lines Cut By A Transversal - Fill ... - Free Printable

Let’s go through each problem one by one. We’ll name the angle pair, say if they’re congruent or supplementary, and find the missing angle x.

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Problem 1)
Angle given: 68°
x is in the same relative position on the other parallel line → Corresponding angles
→ Corresponding angles are congruent when lines are parallel.
So, x = 68°

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Problem 2)
Angles: x° and 134°
They are on the same side of the transversal and between the parallel lines → Same-Side Interior angles
→ Same-Side Interior angles are supplementary (add to 180°)
So, x + 134 = 180
x = 180 - 134 = 46°

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Problem 3)
Angles: x° and 120°
They are opposite each other at the intersection → Vertical angles
→ Vertical angles are always congruent
So, x = 120°

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Problem 4)
Angles: x° and 101°
They are on opposite sides of the transversal and inside the parallel lines → Alternate Interior angles
→ Alternate Interior angles are congruent
So, x = 101°

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Problem 5)
Angles: x° and 77°
They are on the same side of the transversal but outside the parallel lines → Same-Side Exterior angles
→ Same-Side Exterior angles are supplementary
So, x + 77 = 180
x = 180 - 77 = 103°

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Problem 6)
Angles: x° and 106°
They are on opposite sides of the transversal and inside the parallel lines → Alternate Interior angles
→ Congruent
So, x = 106°

*(Note: Even though the diagram might look like it's flipped, as long as they’re alternate interior, they’re equal.)*

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Problem 7)
Angles: x° and 74°
They are on the same side of the transversal and between the parallel lines → Same-Side Interior angles
→ Supplementary
So, x + 74 = 180
x = 180 - 74 = 106°

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Problem 8)
Angles: x° and 142°
They are on opposite sides of the transversal and outside the parallel lines → Alternate Exterior angles
→ Congruent
So, 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°