Measuring Angles: Printable Worksheets - Free Printable

Let’s solve each part step by step.

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First Problem:

We are given:
- ∠ABD = 40°
- ∠ABC = 28°
- We need to find ∠CBD

Look at the diagram (even though we don’t describe it, we can reason from the labels):

Point B is the vertex. Rays go out to A, C, and D. Since ∠ABD is the big angle from A to D, and ∠ABC is part of it (from A to C), then ∠CBD must be the rest — from C to D.

So:

∠CBD = ∠ABD - ∠ABC
∠CBD = 40° - 28° = 12°

✔ That makes sense — if you take away the smaller piece from the bigger piece, you get the leftover piece.

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Second Problem:

We are given:
- ∠EFG = 33°
- ∠GFH = 19°
- We need to find ∠EFH

Again, point F is the vertex. Rays go to E, G, H.

∠EFH is the total angle from E to H. It includes both ∠EFG and ∠GFH.

So:

∠EFH = ∠EFG + ∠GFH
∠EFH = 33° + 19° = 52°

✔ Adding the two parts gives the whole angle.

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Third Problem (Skateboard Ramp):

Original incline = 40°
She adjusts it to half the original incline.

So now:
New incline = 40° ÷ 2 = 20°

✔ Half of 40 is 20 — simple division.

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Final Answer:
∠CBD = 12°
∠EFH = 52°
New ramp incline = 20°