Alternate Angles in Parallel Lines Worksheets - Free Printable

I will solve each of the 9 problems by applying the properties of alternate angles formed when two parallel lines are cut by a transversal.

Key Concepts:

- Alternate Interior Angles are equal.
- Alternate Exterior Angles are equal.
- Corresponding Angles are equal.
- Vertically Opposite Angles are equal.
- Angles on a Straight Line sum to 180°.
- Adjacent Angles (linear pair) sum to 180°.

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Let’s solve each problem one by one.

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Problem 1:

We have two parallel lines cut by a transversal. The angle marked `x` is an alternate interior angle to the 36° angle.

✔ So, x = 36°

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Problem 2:

The angle marked `x` and the 49° angle are vertically opposite or alternate interior? Let’s check:

Actually, the 49° angle and `x` are alternate interior angles, so they are equal.

✔ So, x = 49°

Wait — let me double-check: The 131° angle is adjacent to 49°, so 131° + 49° = 180° → that checks out (linear pair).

Since `x` is alternate interior to 49°, yes:

✔ x = 49°

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Problem 3:

The angle marked `x` is an alternate exterior angle to the 53° angle.

✔ So, x = 53°

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Problem 4:

The 62° angle and the 118° angle are on the same side of the transversal — but wait, 62° + 118° = 180°, so they form a linear pair.

The angle `x` is alternate interior to the 62° angle.

✔ So, x = 62°

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Problem 5:

The 125° angle and the 55° angle are on the same side of the transversal. 125° + 55° = 180° → linear pair.

Angle `x` is alternate interior to the 55° angle.

✔ So, x = 55°

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Problem 6:

The 102° and 78° angles are on the same side of the transversal. 102° + 78° = 180° → linear pair.

Angle `x` is alternate interior to the 78° angle.

✔ So, x = 78°

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Problem 7:

We have two angles: 151° and 29°. Note that 151° + 29° = 180° → linear pair.

Angle `x` is alternate interior to the 29° angle.

✔ So, x = 29°

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Problem 8:

We have two angles: 83° and 97°. 83° + 97° = 180° → linear pair.

Angle `x` is alternate interior to the 83° angle.

✔ So, x = 83°

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Problem 9:

We have 130° and 50°. 130° + 50° = 180° → linear pair.

Angle `x` is alternate interior to the 50° angle.

✔ So, x = 50°

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## ✔ Final Answers:

1) x = 36°
2) x = 49°
3) x = 53°
4) x = 62°
5) x = 55°
6) x = 78°
7) x = 29°
8) x = 83°
9) x = 50°

All answers are based on the property that alternate interior angles are equal when two parallel lines are cut by a transversal. In some cases, we used the fact that adjacent angles on a straight line sum to 180° to identify the correct alternate angle.