Geometry worksheet with angle problems involving intersecting lines and angle calculations.

I will solve this geometry worksheet by analyzing each problem one by one, using the principles of angles formed by intersecting lines and parallel lines.

Let me start with Problem 1.

Problem 1:

- We have two intersecting lines.
- One angle is given as 32°.
- We need to find angles A, B, and C.

From the diagram, I can see that:
- Angle C is vertically opposite to the 32° angle, so they are equal.
- Angles A and B are adjacent to the 32° angle and form a straight line with it.

Using these observations:

Angle C = 32° (vertically opposite angles are equal)

Angle A = 180° - 32° = 148° (angles on a straight line sum to 180°)

Angle B = 148° (vertically opposite to angle A)

So for Problem 1: A = 148°, B = 148°, C = 32°

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Problem 2:

- Two lines intersect.
- One angle is given as 26°.
- We need to find angles A, B, and C.

From the diagram:
- Angle C is vertically opposite to the 26° angle, so they are equal.
- Angles A and B are adjacent to the 26° angle and form a straight line with it.

Using these observations:

Angle C = 26° (vertically opposite angles are equal)

Angle A = 180° - 26° = 154° (angles on a straight line sum to 180°)

Angle B = 154° (vertically opposite to angle A)

So for Problem 2: A = 154°, B = 154°, C = 26°

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Problem 3:

- This appears to be a triangle with some external lines.
- We have angles labeled 120° and 24°.
- We need to find angles A, B, and C.

Looking at the diagram more carefully:
- The 120° angle and angle C are on a straight line, so they are supplementary.
- The 24° angle is an interior angle of the triangle.
- Angle B is vertically opposite to the 24° angle.
- Angle A is an exterior angle to the triangle.

Let me calculate:

Angle C = 180° - 120° = 60° (angles on a straight line sum to 180°)

Angle B = 24° (vertically opposite angles are equal)

Angle A: Since angle A is an exterior angle to the triangle, it equals the sum of the two opposite interior angles. The two opposite interior angles are the 24° angle and angle C (60°).

So, Angle A = 24° + 60° = 84°

Alternatively, we could also think of angle A as being supplementary to the third angle of the triangle. The third angle of the triangle would be 180° - 24° - 60° = 96°, so angle A = 180° - 96° = 84°.

So for Problem 3: A = 84°, B = 24°, C = 60°

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Problem 4:

- We have two parallel lines cut by a transversal.
- One angle is given as 32°.
- We need to find angles A, B, and C.

From the diagram:
- The 32° angle and angle A are vertically opposite, so they are equal.
- Angle B is corresponding to the 32° angle (since the lines are parallel), so they are equal.
- Angle C is adjacent to angle B and forms a straight line with it.

Using these observations:

Angle A = 32° (vertically opposite angles are equal)

Angle B = 32° (corresponding angles are equal when lines are parallel)

Angle C = 180° - 32° = 148° (angles on a straight line sum to 180°)

So for Problem 4: A = 32°, B = 32°, C = 148°

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Final Answers:

1. A = 148°, B = 148°, C = 32°
2. A = 154°, B = 154°, C = 26°
3. A = 84°, B = 24°, C = 60°
4. A = 32°, B = 32°, C = 148°