Geometry worksheet for finding angles formed by intersecting lines and transversals.

Here are the step-by-step solutions for each problem on the worksheet.

1. Find the angles of A, B, and C.

* Angle C: Angles that are opposite each other at an intersection (vertical angles) are equal. Angle C is opposite the $32^\circ$ angle. So, $C = 32^\circ$.
* Angle A: Angles on a straight line add up to $180^\circ$. Angle A and the $32^\circ$ angle form a straight line.
$$180^\circ - 32^\circ = 148^\circ$$
So, $A = 148^\circ$.
* Angle B: Angle B is opposite Angle A (vertical angles), so they are equal. Alternatively, Angle B and the $32^\circ$ angle form a straight line ($180^\circ - 32^\circ = 148^\circ$).
So, $B = 148^\circ$.

2. Find the angles of A, B, and C.

* Angle A: Angle A and the $26^\circ$ angle sit together on a straight line. They must add up to $180^\circ$.
$$180^\circ - 26^\circ = 154^\circ$$
So, $A = 154^\circ$.
* Angle B: Angle B is vertically opposite the $26^\circ$ angle. Vertical angles are always equal.
So, $B = 26^\circ$.
* Angle C: Angle C is vertically opposite Angle A. Since $A = 154^\circ$, then C is also $154^\circ$.
So, $C = 154^\circ$.

3. Find the angles of A, B, and C.

This problem involves a triangle formed by intersecting lines.
* Angle C: Look at the bottom left intersection. Angle C and the $120^\circ$ angle are on a straight line.
$$180^\circ - 120^\circ = 60^\circ$$
So, $C = 60^\circ$.
* Angle B: Now look at the triangle in the middle. The angles inside any triangle always add up to $180^\circ$. We know two angles: Angle C ($60^\circ$) and the angle on the right ($24^\circ$).
$$180^\circ - 60^\circ - 24^\circ = 96^\circ$$
So, $B = 96^\circ$.
* Angle A: Angle A and Angle B are on a straight line.
$$180^\circ - 96^\circ = 84^\circ$$
So, $A = 84^\circ$.

4. Find the angles of A, B, and C.

The arrows on the horizontal lines indicate that they are parallel.
* Angle A: Angle A and the $32^\circ$ angle are "corresponding angles" (they are in the same position relative to the parallel lines). Corresponding angles are equal.
So, $A = 32^\circ$.
* Angle C: Angle C and Angle A are "alternate interior angles" (inside the parallel lines, on opposite sides of the transversal). These are also equal. Or, you can see that Angle C corresponds to the $32^\circ$ angle as well.
So, $C = 32^\circ$.
* Angle B: Angle B and Angle C are on a straight line.
$$180^\circ - 32^\circ = 148^\circ$$
So, $B = 148^\circ$.

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Final Answer:
1. A = 148°, B = 148°, C = 32°
2. A = 154°, B = 26°, C = 154°
3. A = 84°, B = 96°, C = 60°
4. A = 32°, B = 148°, C = 32°