Geometry Angles Worksheet | Worksheets Worksheets - Free Printable

Let’s solve each problem step by step.

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Problem 1:

We are given two lines intersecting, forming angles A, B, and C. One angle is labeled 32°.

- Angle C is vertically opposite to the 32° angle → so C = 32°
- Angles A and C are on a straight line → they add up to 180° → A = 180° - 32° = 148°
- Angle B is vertically opposite to angle A → so B = 148°

Wait — let’s double-check the diagram logic.

Actually, looking at standard labeling:

The 32° angle and angle C are adjacent? Or vertical?

In typical diagrams like this:

If two lines cross, they form 4 angles. The 32° is one of them. Then:

- Angle directly across (vertical) from 32° is also 32° → that’s likely angle C.
- Angles next to it (adjacent on straight line) are 180° - 32° = 148° → those would be A and B.

But in the diagram, A and B are on the same side of the transversal? Actually, no — since it's just two lines crossing, all four angles are around the point.

Standard rule: Vertical angles are equal. Adjacent angles on a straight line sum to 180°.

So if 32° is given, then:

→ The angle opposite it (let’s say C) = 32°
→ The two adjacent angles (A and B) = 180° - 32° = 148° each

Yes. So:

A = 148°, B = 148°, C = 32°

But wait — maybe A and B are not both 148°? Let me think again.

Actually, when two lines intersect, there are two pairs of vertical angles.

Suppose the 32° angle is bottom-left.

Then top-right is also 32° (vertical).

Top-left and bottom-right are each 180° - 32° = 148°.

Now, how are A, B, C labeled?

From the diagram description (even though I can’t see it, based on common worksheets):

Usually, A and B are the larger angles, C is the smaller one matching the given.

So yes:

Answer for #1: A = 148°, B = 148°, C = 32°

But let’s confirm with Problem 2 to see pattern.

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Problem 2:

Given 26°, find A, B, C.

Same setup: two lines intersecting.

Assume 26° is one angle.

Then vertical angle = 26° → probably C.

Adjacent angles = 180° - 26° = 154° → A and B.

So:

A = 154°, B = 154°, C = 26°

Makes sense.

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Problem 3:

This one has a triangle! And an exterior angle.

We have a triangle with one interior angle 24°, and an exterior angle at another vertex labeled 120°.

Angle C is inside the triangle, adjacent to the 120° exterior angle.

So:

Exterior angle = sum of two remote interior angles.

Or: interior + exterior = 180° (linear pair)

So angle C (interior) = 180° - 120° = 60°

Now, in the triangle, we have:

- One angle = 24°
- Another angle = C = 60°
- Third angle = ? Let’s call it X

Sum of triangle angles = 180°

So X = 180° - 24° - 60° = 96°

Now, what are A and B?

Looking at diagram description: A and B are angles formed by the intersecting lines outside the triangle.

Specifically, angle A is probably vertical to the 96° angle we just found → so A = 96°

Angle B is adjacent to A on a straight line → so B = 180° - 96° = 84°

Wait — let’s map carefully.

At the top intersection (where lines cross above the triangle), we have angles A and B.

One of the angles in the triangle at that vertex is 96° (we calculated). That 96° angle and angle A are vertical angles → so A = 96°

Then angle B is adjacent to A → so B = 180° - 96° = 84°

And angle C we already have as 60° (from linear pair with 120°)

So:

A = 96°, B = 84°, C = 60°

Check: In triangle: 24° + 60° + 96° = 180° ✓

Exterior angle 120° = 24° + 96°? 24+96=120 ✓ Perfect.

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Problem 4:

Two parallel lines cut by a transversal. Arrows indicate parallel lines.

Given angle at bottom left is 32°, labeled near A.

We need to find A, B, C.

First, angle A: it’s the angle shown as 32°? Or is 32° adjacent?

Diagram says: “A / 32°” — likely angle A is 32°, or the 32° is part of angle A.

Typical labeling: if it says “A / 32°”, it might mean angle A is 32°.

But let’s assume the 32° is the measure of the angle at the lower intersection, between the transversal and the lower parallel line.

Since lines are parallel:

Corresponding angles are equal.

Alternate interior angles are equal.

Consecutive interior angles sum to 180°.

Let’s define:

At lower intersection: angle between transversal and lower line is 32°. Let’s say that’s angle A.

Then, angle C is on the same side, between the two parallels — consecutive interior angle → so C = 180° - 32° = 148°

Angle B is at the upper intersection, corresponding to angle A → so B = 32°

Wait — but in the diagram, B and C are at the same intersection? Probably.

Standard: when a transversal cuts two parallels, at each intersection, four angles.

At lower intersection: one angle is 32° (say, angle A).

Then the adjacent angle on the straight line is 180° - 32° = 148° — that could be angle C? But C is labeled at the upper intersection? No.

Looking back: in problem 4, labels are:

- A at lower left
- B and C at upper intersection

Probably:

Angle A = 32° (given)

Since lines are parallel, the corresponding angle at upper intersection (same relative position) is also 32° — that might be angle B.

Then angle C is adjacent to B on the straight line → so C = 180° - 32° = 148°

Alternatively, angle C could be alternate interior to A → which would also be 32°, but that doesn't match labeling.

Better approach:

Assume:

- Angle A is the 32° angle at the lower intersection.
- Angle B is the corresponding angle at the upper intersection → so B = 32°
- Angle C is the adjacent angle to B at the upper intersection → so C = 180° - 32° = 148°

Yes, that makes sense.

Sometimes C is the consecutive interior angle to A, which would be 180° - 32° = 148°, and that matches.

So:

A = 32°, B = 32°, C = 148°

But let’s verify with standard rules.

If A is 32°, and it’s an acute angle between transversal and lower line.

Then the angle directly above it (corresponding) is also 32° — that’s B.

Then the angle next to B (on the straight line) is 148° — that’s C.

Perfect.

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Now, compiling all answers:

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

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

Problem 3:
A = 96°, B = 84°, C = 60°

Problem 4:
A = 32°, B = 32°, C = 148°

I’ll write them clearly.

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