Reading Protractor interactive worksheet - Free Printable

I'll solve this protractor reading problem step by step. Let me work through each angle measurement carefully.

Looking at the protractor:
- Point A is at the center (vertex)
- The baseline goes from B (left, 180° on inner scale, 0° on outer scale) to Z (right, 0° on inner scale, 180° on outer scale)
- I need to read angles using the appropriate scale

Let me identify where each letter points and calculate the angles:

For angles starting with B (using outer scale from left):
- B = 0° (baseline left)
- C ≈ 10°
- D ≈ 20°
- E ≈ 30°
- F ≈ 40°
- G ≈ 50°
- H ≈ 60°
- J ≈ 70°
- K ≈ 80°
- L ≈ 90°
- M ≈ 95°
- N ≈ 100°
- P ≈ 105°
- Q ≈ 110°
- R ≈ 120°
- S ≈ 130°
- T ≈ 140°
- U ≈ 150°
- V ≈ 160°
- W ≈ 170°
- X ≈ 175°
- Y ≈ 178°
- Z = 180° (baseline right)

Now let me calculate each angle:

1) ∠BAC: From B(0°) to C(10°) = 10°
2) ∠BAE: From B(0°) to E(30°) = 30°
3) ∠BAG: From B(0°) to G(50°) = 50°
4) ∠BAK: From B(0°) to K(80°) = 80°
5) BAP: From B(0°) to P(105°) = 105°
6) ∠BAR: From B(0°) to R(120°) = 120°
7) ∠BAT: From B(0°) to T(140°) = 140°
8) ∠BAX: From B(0°) to X(175°) = 175°

For angles starting with Z (using inner scale from right):
9) ∠ZAY: From Z(0°) to Y(2°) = 2°
10) ∠ZAW: From Z(0°) to W(10°) = 10°
11) ∠ZAU: From Z(0°) to U(30°) = 30°
12) ZAS: From Z(0°) to S(50°) = 50°
13) ∠ZAQ: From Z(0°) to Q(70°) = 70°
14) ∠ZAC: From Z(0°) to C(170°) = 170°
15) ∠ZAH: From Z(0°) to H(120°) = 120°
16) ∠ZAL: From Z(0°) to L(90°) = 90°

Other angles:
17) ∠CAD: From C(10°) to D(20°) = 10°
18) ∠EAF: From E(30°) to F(40°) = 10°
19) ∠BAZ: From B(0°) to Z(180°) = 180°
20) ∠JAY: From J(70°) to Y(178°) = 108°

Wait, let me reconsider #20. Looking more carefully at the positions...

Actually, let me be more precise. Let me look at the actual ray positions again:

From the diagram:
- Rays are labeled around the semicircle
- Each major tick mark appears to be 10 degrees

Let me recalculate more carefully:

21) ∠LAP: L is at 90°, P is at 105°. So ∠LAP = 105° - 90° = 15°
22) ∠PAR: P is at 105°, R is at 120°. So ∠PAR = 120° - 105° = 15°
23) ∠SAW: S is at 130°, W is at 170°. So ∠SAW = 170° - 130° = 40°
24) ∠KAT: K is at 80°, T is at 140°. So ∠KAT = 140° - 80° = 60°
25) ∠HAN: H is at 60°, N is at 100°. So ∠HAN = 100° - 60° = 40°
26) ∠CAY: C is at 10°, Y is at 178°. So ∠CAY = 178° - 10° = 168°
27) ∠VAN: V is at 160°, N is at 100°. So ∠VAN = 160° - 100° = 60°
28) ∠RAQ: R is at 120°, Q is at 110°. So ∠RAQ = 120° - 110° = 10°
29) ∠DAX: D is at 20°, X is at 175°. So ∠DAX = 175° - 20° = 155°
30) UAF: U is at 150°, F is at 40°. So ∠UAF = 150° - 40° = 110°
31) ∠VAM: V is at 160°, M is at 95°. So ∠VAM = 160° - 95° = 65°
32) ∠RAG: R is at 120°, G is at 50°. So ∠RAG = 120° - 50° = 70°

Let me verify a few key measurements by looking at the protractor more carefully:

Looking at the spacing between letters, they appear to be approximately 10° apart for most, but some might be different. Let me check the pattern more systematically.

Actually, looking at the diagram more carefully:
- The rays seem to be spaced at regular intervals
- From B to Z is 180° total
- Counting the rays/letters: B, C, D, E, F, G, H, J, K, L, M, N, P, Q, R, S, T, U, V, W, X, Y, Z

That's 23 rays over 180°, which would be about 7.8° apart on average, but they're not all evenly spaced.

Let me use the degree markings visible on the protractor to determine exact positions:

From the inner scale (reading from right/Z going counterclockwise):
- Z = 0°
- Y ≈ 2°
- X ≈ 5°
- W ≈ 10°
- V ≈ 20°
- U ≈ 30°
- T ≈ 40°
- S ≈ 50°
- R ≈ 60°
- Q ≈ 70°
- P ≈ 75°
- N ≈ 80°
- M ≈ 85°
- L = 90°
- K ≈ 100°
- J ≈ 110°
- H ≈ 120°
- G ≈ 130°
- F ≈ 140°
- E ≈ 150°
- D ≈ 160°
- C ≈ 170°
- B = 180°

Wait, I think I've been confusing myself with the scales. Let me start fresh and be very systematic.

The protractor has TWO scales:
- OUTER scale: 0° at left (B), increases to 180° at right (Z)
- INNER scale: 180° at left (B), decreases to 0° at right (Z)

For angles like ∠BAC, we measure from ray AB to ray AC. Since B is on the left baseline, we use the OUTER scale.

Let me read the positions more carefully from the image:

Using OUTER scale (0° at B/left, increasing clockwise):
- B = 0°
- C ≈ 10°
- D ≈ 20°
- E ≈ 30°
- F ≈ 40°
- G ≈ 50°
- H ≈ 60°
- J ≈ 70°
- K ≈ 80°
- L = 90°
- M ≈ 95°
- N ≈ 100°
- P ≈ 105°
- Q ≈ 110°
- R ≈ 120°
- S ≈ 130°
- T ≈ 140°
- U ≈ 150°
- V ≈ 160°
- W ≈ 170°
- X ≈ 175°
- Y ≈ 178°
- Z = 180°

Now calculating all answers:

1) ∠BAC = 10° - 0° = 10°
2) ∠BAE = 30° - 0° = 30°
3) ∠BAG = 50° - 0° = 50°
4) ∠BAK = 80° - 0° = 80°
5) ∠BAP = 105° - 0° = 105°
6) ∠BAR = 120° - 0° = 120°
7) ∠BAT = 140° - 0° = 140°
8) ∠BAX = 175° - 0° = 175°

9) ∠ZAY: Using inner scale, Z=0°, Y≈2°, so 2°
10) ∠ZAW: Z=0°, W≈10°, so 10°
11) ∠ZAU: Z=0°, U≈30°, so 30°
12) ∠ZAS: Z=0°, S≈50°, so 50°
13) ∠ZAQ: Z=0°, Q≈70°, so 70°
14) ∠ZAC: Z=0°, C≈170°, so 170°
15) ∠ZAH: Z=0°, H≈120°, so 120°
16) ∠ZAL: Z=0°, L=90°, so 90°

17) ∠CAD: C≈10°, D≈20°, so 20°-10° = 10°
18) ∠EAF: E≈30°, F≈40°, so 40°-30° = 10°
19) ∠BAZ: B=0°, Z=180°, so 180°
20) ∠JAY: J≈70°, Y≈178°, so 178°-70° = 108°

21) ∠LAP: L=90°, P≈105°, so 105°-90° = 15°
22) ∠PAR: P≈105°, R≈120°, so 120°-105° = 15°
23) ∠SAW: S≈130°, W≈170°, so 170°-130° = 40°
24) ∠KAT: K≈80°, T≈140°, so 140°-80° = 60°
25) ∠HAN: H≈60°, N≈100°, so 100°-60° = 40°
26) ∠CAY: C≈10°, Y≈178°, so 178°-10° = 168°
27) ∠VAN: V≈160°, N≈100°, so 160°-100° = 60°
28) ∠RAQ: R≈120°, Q≈110°, so 120°-110° = 10°
29) ∠DAX: D≈20°, X≈175°, so 175°-20° = 155°
30) UAF: U≈150°, F≈40°, so 150°-40° = 110°
31) ∠VAM: V≈160°, M≈95°, so 160°-95° = 65°
32) ∠RAG: R≈120°, G≈50°, so 120°-50° = 70°

Final Answer:
1) 10° 2) 30° 3) 50° 4) 80° 5) 105° 6) 120° 7) 140° 8) 175°
9) 2° 10) 10° 11) 30° 12) 50° 13) 70° 14) 170° 15) 120° 16) 90°
17) 10° 18) 10° 19) 180° 20) 108°
21) 15° 22) 15° 23) 40° 24) 60° 25) 40° 26) 168° 27) 60° 28) 10°
29) 155° 30) 110° 31) 65° 32) 70°