Geometry Worksheets | Angles Worksheets - Free Printable

To find the measure of each angle, we need to read the protractor carefully. The protractor has two sets of numbers: one going from 0 to 180 on the top (red) and one from 0 to 180 on the bottom (black). We’ll use the scale that starts at 0° on the side where the angle begins.

All angles start at point A, with ray AF as the baseline (0° on the right side). So for any angle like ∠EAF, we look at where ray AE points on the protractor — using the bottom scale (since it starts at 0° on the right).

Let’s go one by one:

∠CAB:
Ray AC is pointing to about 170° on the bottom scale? Wait — no. Actually, since AB is on the left (180° on bottom scale), and AC is close to AB, we should measure from AB to AC. But standard way: if we’re measuring ∠CAB, vertex is A, rays are AC and AB. Since AB is along the straight line to the left, and AC is just above it, we can see AC is at approximately 170° on the *top* scale? Let me think again.

Actually, better approach:
The protractor is placed with center at A, and baseline AF to the right (0° on bottom scale). So:

- Ray AF → 0° (bottom scale)
- Ray AE → looks like 40° on bottom scale → so ∠EAF = 40°
- Ray AD → looks like 70° on bottom scale → so ∠DAF = 70°
- Ray AC → looks like 170° on bottom scale? That would be almost 180°, but let's check top scale.

Wait — actually, for angles measured from the left (like ∠CAB), we might need to use the top scale.

Let me reorient:

Standard protractor reading:
- If you measure from the right (AF), use the bottom numbers (0° on right).
- If you measure from the left (AB), use the top numbers (0° on left).

But all angles here are named with A as vertex, and the first letter is the other end.

So:

∠CAB: from CA to BA. BA is the leftward ray (180° on bottom scale, or 0° on top scale). CA is pointing to about 10° on the top scale? Let’s look:

Looking at the diagram:

- Point C is near the left edge. On the top scale (which goes 0° at left to 180° at right), point C is at about 10°. So from AB (which is 0° on top scale) to AC is 10°. So ∠CAB = 10°.

Wait — that makes sense because in the second diagram, it’s clearer. In both diagrams, the lines are the same.

Let me list all rays and their positions using the bottom scale (0° at right, increasing counterclockwise):

- AF → 0°
- AE → 40° (because it’s at 40 on bottom scale)
- AD → 70° (on bottom scale)
- AC → 170° (on bottom scale) — because it’s near the left, 10° from 180°
- AB → 180°

Now, to find an angle between two rays, subtract the smaller degree from the larger.

For example:

∠EAF: between AE (40°) and AF (0°) → 40° - 0° = 40°

∠DAF: between AD (70°) and AF (0°) → 70° - 0° = 70°

∠CAF: between AC (170°) and AF (0°) → 170° - 0° = 170°

∠DAB: between AD (70°) and AB (180°) → 180° - 70° = 110°

∠EAB: between AE (40°) and AB (180°) → 180° - 40° = 140°

∠CAB: between AC (170°) and AB (180°) → 180° - 170° = 10°

Now, let’s verify with the top scale to make sure.

Top scale: 0° at left (AB), 180° at right (AF)

So:

- AB → 0° (top)
- AC → 10° (top) → so ∠CAB = 10° ✓
- AD → 110° (top) → so ∠DAB = 110° ✓
- AE → 140° (top) → so ∠EAB = 140° ✓
- AF → 180° (top)

Then:

∠CAF: from AC (10° top) to AF (180° top) → 180° - 10° = 170° ✓

∠DAF: from AD (110° top) to AF (180° top) → 180° - 110° = 70° ✓

∠EAF: from AE (140° top) to AF (180° top) → 180° - 140° = 40° ✓

Perfect, consistent.

So final answers:

∠CAB = 10°
∠DAB = 110°
∠EAB = 140°
∠CAF = 170°
∠DAF = 70°
∠EAF = 40°

These are the same for both diagrams since the lines are identical.

Final Answer:
∠CAB = 10°, ∠DAB = 110°, ∠EAB = 140°, ∠CAF = 170°, ∠DAF = 70°, ∠EAF = 40°