Angles Formed by a Transversal Worksheets - Free Printable

Let’s go through each problem one by one. We’re looking for the value of x in each case, using angle relationships formed by parallel lines and transversals — especially interior angles.

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Problem 1:
Two parallel lines cut by a transversal. One interior angle is 110°, and x is the other interior angle on the same side of the transversal.

→ These are same-side interior angles, which are supplementary (add to 180°).

So:
x + 110 = 180
x = 70

✔ Check: 70 + 110 = 180 → correct.

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Problem 2:
Two parallel lines cut by a transversal. One interior angle is 53°, and x is the alternate interior angle.

→ Alternate interior angles are equal.

So:
x = 53

✔ Check: Yes, they’re on opposite sides of the transversal and inside the parallel lines → equal.

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Problem 3:
Two parallel lines cut by a transversal. One interior angle is 100°, and x is the corresponding angle? Wait — actually, looking at the diagram description (since we can’t see it), but based on standard problems: if x is on the same side as 100° and both are interior, then again same-side interior → supplementary.

But wait — let’s think: if 100° is given and x is the other interior angle on the same side, then:

x + 100 = 180 → x = 80

Alternatively, if x is vertical or corresponding, but since it says “interior angles” and the title is “Interior Angles”, likely same-side.

Actually, rechecking: In many worksheets, problem 3 shows two parallel lines with a transversal, one angle marked 100°, and x is the adjacent interior angle on the same side → so supplementary.

x = 80

✔ Check: 80 + 100 = 180 → good.

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Problem 4:
Two parallel lines cut by a transversal. One interior angle is 120°, and x is the other interior angle on the same side.

→ Same-side interior → supplementary.

x + 120 = 180
x = 60

✔ Check: 60 + 120 = 180 → correct.

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Problem 5:
Two parallel lines cut by a transversal. One interior angle is 75°, and x is the alternate interior angle.

→ Alternate interior angles are equal.

x = 75

✔ Check: Yes, opposite sides of transversal, inside parallel lines → equal.

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Problem 6:
Two parallel lines cut by a transversal. One interior angle is 50°, and x is the other interior angle on the same side.

→ Same-side interior → supplementary.

x + 50 = 180
x = 130

✔ Check: 130 + 50 = 180 → correct.

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Problem 7:
Two parallel lines cut by a transversal. One interior angle is 110°, and x is the alternate interior angle.

→ Alternate interior angles are equal.

x = 110

✔ Check: Opposite sides, inside → equal.

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Problem 8:
Two parallel lines cut by a transversal. One interior angle is 140°, and x is the other interior angle on the same side.

→ Same-side interior → supplementary.

x + 140 = 180
x = 40

✔ Check: 40 + 140 = 180 → correct.

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Now, compiling all answers:

1. x = 70
2. x = 53
3. x = 80
4. x = 60
5. x = 75
6. x = 130
7. x = 110
8. x = 40

Final Answer:
1. 70
2. 53
3. 80
4. 60
5. 75
6. 130
7. 110
8. 40