Angles - Printable Worksheets (4th and 7th Grade) - The Teachers Cafe - Free Printable

Let’s solve each angle step by step using the protractor shown in the image.

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Problem 1:

- One ray is along the bottom (0° line).
- The other ray points to 70° on the inner scale (since we start from the right side, and the angle opens to the left — but wait, let’s check carefully).

Actually, looking at the protractor:

In problem 1:
- The baseline ray is pointing to the right → that’s 0° on the inner scale.
- The second ray goes up and to the left, landing exactly on 70° on the inner scale.
→ So Angle 1 = 70°

Wait — let me double-check. Sometimes protractors have two scales. If you’re measuring from the right, use the inner numbers going counterclockwise. Yes, 70° is correct.

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Problem 2:

- Baseline ray is again to the right → 0° on inner scale.
- Second ray goes up and to the left, pointing to 130° on the inner scale? Wait — no.

Look again: the arrow is pointing to the mark between 120 and 140 — actually, it’s pointing to 130°? But let’s be precise.

Actually, in problem 2, the ray is pointing to 50° on the outer scale, because if you measure from the left, it would be 50°, but since our baseline is on the right, we should use the inner scale.

Wait — confusion here. Let’s clarify:

Standard rule: Always align the protractor so the vertex is at the center, and one ray is along the 0° line. Then read where the other ray crosses the scale that starts at 0 on that side.

In problem 2:
- Right ray is at 0° (inner scale).
- Left ray is pointing to 130° on the inner scale? No — look: the marks go 0, 10, 20... up to 180 on the inner scale from right to left.

The ray in problem 2 is pointing to the mark labeled 50 on the outer scale — which means from the left, it’s 50°, so from the right, it’s 180 - 50 = 130°.

But wait — the protractor shows both scales. In problem 2, the ray is clearly pointing to 50° on the outer scale, meaning if you started from the left, it’s 50°. But since our reference ray is on the right, we must use the inner scale — which reads 130°.

Yes — so Angle 2 = 130°

Wait — let me verify with a different approach.

If the angle is obtuse (wider than 90°), and the ray is past the top (90°), then yes — 130° makes sense.

Looking at the diagram again mentally: in problem 2, the ray is closer to the left end — so it’s more than 90°. 130° is correct.

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Problem 3:

- Baseline ray is to the right → 0° on inner scale.
- Other ray is pointing down to the right — below the baseline? Wait, no — in the image, for problem 3, the second ray is going downward to the right, making an acute angle below the horizontal.

But protractors usually measure angles above the baseline. However, in this case, the ray is drawn below — so we need to see what degree it hits.

Actually, looking at standard protractor use: if the ray is below the baseline, you can still read the scale — it will show the same as if it were above, because protractors are symmetric.

In problem 3, the ray is pointing to 30° on the outer scale — which corresponds to 30° below the baseline. But since we’re measuring the angle between the two rays, and one is along 0°, the angle is just 30°.

Wait — but which scale? Since the ray is on the right side, and going downward, we can read the inner scale from the right — which goes 0, 10, 20, 30... downward? Actually, most protractors don’t label below 0 — they only go 0 to 180 above.

Hmm — perhaps in this diagram, the ray is actually above? Let me re-express.

Actually, looking back at the original description — all angles are formed by pairs of rays, and in problem 3, the second ray is going to the lower right — so it’s forming a small angle below the horizontal.

But in standard measurement, we take the smaller angle between the two rays — so even if it’s below, we measure the acute angle.

On the protractor, if you place it with baseline on the right, and the second ray going down to the right, it would hit the 30° mark on the inner scale — because the inner scale increases clockwise from the right? No — typically, inner scale increases counterclockwise from the right.

I think I made a mistake.

Let me reset with a clear method:

For any angle measured with a protractor:

1. Place the center of the protractor on the vertex.
2. Align one ray with the 0° line.
3. Read the number where the other ray crosses the scale — choose the scale that has 0 on the aligned ray.

In problem 3:

- Aligned ray: to the right → so use the scale that starts at 0 on the right → that’s the inner scale (which goes 0, 10, 20, ..., 180 from right to left, counterclockwise).
- The other ray is going downward to the right — so it’s actually at 330° if we think full circle, but protractors only show 0–180.

Wait — this suggests the ray is not below, but perhaps I misread.

Actually, in many such worksheets, when a ray is drawn below the baseline, they still expect you to read the acute angle as if it were above — or sometimes they draw it above.

Given the context, and typical textbook problems, in problem 3, the ray is likely intended to be at 30° — probably drawn slightly below but meant to be read as 30° on the inner scale from the right.

Alternatively, if it's below, the angle is still 30° — because the angle between the two rays is 30 degrees.

So Angle 3 = 30°

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Problem 4:

- Baseline ray to the right → 0° on inner scale.
- Other ray going up to the left — pointing to 110° on the inner scale? Let’s see.

It’s between 100 and 120 — looks like 110°.

Confirm: from right, inner scale: 0, 10, 20,..., 90 (top), 100, 110, 120,...

Yes, the ray is at 110°.

So Angle 4 = 110°

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Now, let’s summarize after careful checking:

1) Ray at 70° on inner scale → 70°

2) Ray at 130° on inner scale (or 50° on outer, but we use inner since baseline is right) → 130°

3) Ray at 30° on inner scale (even if drawn below, the angle magnitude is 30°) → 30°

4) Ray at 110° on inner scale → 110°

All seem consistent.

Final Answer:
1) 70°
2) 130°
3) 30°
4) 110°