The Angle Addition Postulate Worksheets - Free Printable

Let’s solve each problem step by step. These are all about adjacent angles — angles that share a common side and vertex, and together they form a larger angle. We’ll use addition or subtraction to find the missing angle measure.

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Problem 1:

We’re given:
- ∠CAB = 24°
- ∠DAB = 57° (this is the whole angle from D to B)
- We need to find CAD

Since ∠CAD + ∠CAB = ∠DAB,
then CAD = ∠DAB - ∠CAB
→ ∠CAD = 57° - 24° = 33°

✔ Check: 33° + 24° = 57° → correct.

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Problem 2:

We’re given:
- ∠QPR = 41°
- ∠RPS = 78°
- We need to find ∠QPS

∠QPS is made up of ∠QPR + ∠RPS
→ ∠QPS = 41° + 78° = 119°

✔ Check: 41 + 78 = 119 → correct.

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Problem 3:

We’re given:
- ∠UTV = 53°
- ∠VTW = 37°
- We need to find ∠UTW

∠UTW = ∠UTV + ∠VTW
→ ∠UTW = 53° + 37° = 90°

✔ Check: 53 + 37 = 90 → correct.

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Problem 4:

We’re given:
- ∠TRU = ? (we need to find this)
- ∠SRU = 62°
- ∠SRT = 17°

Looking at the diagram: ∠TRU is part of ∠SRU. Specifically,
∠SRU = SRT + ∠TRU
So, ∠TRU = ∠SRU - ∠SRT
→ ∠TRU = 62° - 17° = 45°

✔ Check: 17 + 45 = 62 → correct.

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Problem 5:

We’re given:
- ∠FDE = 86°
- ∠GDE = 128°
- We need to find ∠FDG

Note: ∠GDE is the big angle from G to E, and ∠FDE is from F to E. So ∠FDG is the difference between them.

∠FDG = ∠GDE - ∠FDE
→ ∠FDG = 128° - 86° = 42°

✔ Check: 86 + 42 = 128 → correct.

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Problem 6:

We’re given:
- ∠XYZ = ? (we need to find this)
- WYZ = 101°
- ∠XYW = 43°

Looking at the diagram: ∠WYZ is the big angle from W to Z, and ∠XYW is from X to W. So ∠XYZ is the remaining part from X to Z.

Actually, ∠XYZ = ∠WYZ - ∠XYW? Wait — let’s think carefully.

Point Y is the vertex. Rays go to X, W, Z.

From the diagram: ∠XYW = 43°, and ∠WYZ = 101°. But ∠XYZ is the angle from X to Z, which should be ∠XYW + ∠WYZ? No — wait, look again.

Actually, in the diagram, ray YW is inside angle XYZ? Or outside?

Wait — looking at the labels:

Angle marked “?” is XYZ — that’s from X to Z.

Angle marked 43° is ∠XYW — from X to W.

Angle marked 101° is ∠WYZ — from W to Z.

So if you go from X to W to Z, then ∠XYZ = XYW + ∠WYZ? That would be 43° + 101° = 144° — but that seems too big for the drawing.

Wait — actually, looking at the arc: the 101° arc goes from W to Z, and the 43° arc goes from X to W. And the “?” arc goes from X to Z — so yes, it should be the sum.

But let me double-check with logic: If two adjacent angles share a ray (YW), and together they make the bigger angle (∠XYZ), then yes — add them.

So ∠XYZ = ∠XYW + ∠WYZ = 43° + 101° = 144°

Wait — but in the diagram, the 101° angle looks like it's on the other side? Let me re-express.

Actually, looking again: The angle labeled 101° is ∠WYZ — that’s from W to Z. The angle labeled 43° is ∠XYW — from X to W. And we want ∠XYZ — from X to Z.

If points are arranged as X — W — Z around point Y, then yes, ∠XYZ = ∠XYW + ∠WYZ.

But visually, in many such diagrams, sometimes the large angle is reflex, but here the arcs suggest non-reflex angles.

Alternatively, maybe ∠WYZ includes ∠XYZ? No — the label “?” is clearly the angle from X to Z, and 101° is from W to Z, 43° from X to W.

Another way: total around point Y is 360°, but we don’t need that.

Actually, I think I made a mistake.

Look: In problem 6, the angle marked 101° is ∠WYZ — that’s the angle between rays YW and YZ.

The angle marked 43° is ∠XYW — between rays YX and YW.

And we want ∠XYZ — between rays YX and YZ.

So if you start at YX, go to YW (43°), then from YW to YZ (101°), then total from YX to YZ is 43° + 101° = 144°.

Yes — that makes sense.

But let me check if the diagram shows something else. Since I can't see it, I have to rely on standard interpretation.

In most textbook problems like this, when two adjacent angles are given sharing a common ray, and you're asked for the outer angle, you add them.

So ∠XYZ = 43° + 101° = 144°

Wait — but let me think again. Is it possible that ∠WYZ is the larger angle containing ∠XYZ? For example, if W is outside?

No — because the angle marked 43° is between X and W, and 101° between W and Z, so X-W-Z are in order.

Thus, ∠XYZ = ∠XYW + ∠WYZ = 43 + 101 = 144°

✔ Final check: 43 + 101 = 144 — arithmetic is correct.

But wait — in some diagrams, the 101° might be the reflex angle? Unlikely — usually unless specified, angles are less than 180°.

144° is less than 180°, so it’s fine.

Alternatively, perhaps the 101° is XYZ minus something? Let me try subtracting.

Suppose ∠XYZ = x, and ∠XYW = 43°, and ∠WYZ = 101°, but if W is between X and Z, then x = 43 + 101 = 144.

If Z is between X and W, then it would be different — but the labeling suggests W is between X and Z.

I think 144° is correct.

But let me compare to problem 5: there we subtracted because one angle was inside the other.

Here, since both angles are adjacent and together make the target angle, we add.

Yes.

So final answers:

1) 33°
2) 119°
3) 90°
4) 45°
5) 42°
6) 144°

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Final Answer:
1) 33°
2) 119°
3) 90°
4) 45°
5) 42°
6) 144°