Geometry worksheet with angle calculation problems.

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

Problem 1

Goal: Find angles A, B, and C.
* Angle A: Angles on a straight line add up to $180^\circ$. The angle next to A is $32^\circ$.
$$180^\circ - 32^\circ = 148^\circ$$
So, $A = 148^\circ$.
* Angle B: Angle B and the $32^\circ$ angle are "vertical angles" (they are opposite each other). Vertical angles are always equal.
So, $B = 32^\circ$.
* Angle C: Angle C and Angle A are vertical angles, so they are equal. Alternatively, Angle C and the $32^\circ$ angle form a straight line ($180^\circ - 32^\circ$).
So, $C = 148^\circ$.

Problem 2

Goal: Find angles A, B, and C.
* Angle A: Angle A and the $26^\circ$ angle are 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 to the $26^\circ$ angle. Therefore, it is equal.
So, $B = 26^\circ$.
* Angle C: Angle C is vertically opposite to Angle A. Therefore, it is equal to A.
So, $C = 154^\circ$.

Problem 3

Goal: Find angles A, B, and C.
* Angle C: Angle C and the $120^\circ$ angle are on a straight line.
$$180^\circ - 120^\circ = 60^\circ$$
So, $C = 60^\circ$.
* Angle B: Look at the triangle formed in the middle. The angles inside a triangle always add up to $180^\circ$. We know two angles: $C$ (which is $60^\circ$) and the one labeled $24^\circ$.
$$180^\circ - 60^\circ - 24^\circ = 96^\circ$$
So, $B = 96^\circ$.
* Angle A: Angle A and Angle B are on a straight line.
$$180^\circ - 96^\circ = 84^\circ$$
So, $A = 84^\circ$.

Problem 4

Goal: Find angles A, B, and C.
*Note: 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 at each intersection where the diagonal line crosses the parallel lines). Corresponding angles are equal.
So, $A = 32^\circ$.
* Angle C: Angle C and Angle A are "consecutive interior angles" (they are on the same side of the transversal and between the parallel lines). These angles add up to $180^\circ$.
$$180^\circ - 32^\circ = 148^\circ$$
So, $C = 148^\circ$.
* Angle B: Angle B and Angle C are on a straight line.
$$180^\circ - 148^\circ = 32^\circ$$
So, $B = 32^\circ$.

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