Grade 6 geometry worksheet focusing on finding the measures of angles formed by intersecting lines.

Let’s solve each problem one by one. We’ll use the idea that when angles are next to each other and share a side, we can add or subtract them to find missing measures.

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Problem 1:

We see angle DAB is made of two parts: angle CAD (which we need to find) and angle CAB = 24°.
The whole angle DAB is labeled as 57°.

So:
m∠CAD + m∠CAB = m∠DAB
→ m∠CAD + 24° = 57°
→ m∠CAD = 57° - 24° = 33°

✔ Check: 33 + 24 = 57 → Correct.

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Problem 2:

Angle QPS is made of two parts: angle QPR = 41° and angle RPS = 78°.
They are adjacent and together form angle QPS.

So:
m∠QPS = 41° + 78° = 119°

✔ Check: 41 + 78 = 119 → Correct.

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Problem 3:

Angle UTW is a right angle (marked with square corner), so it’s 90°.
It’s split into angle UTV (what we want) and angle VTW = 37°.

So:
m∠UTV + 37° = 90°
→ m∠UTV = 90° - 37° = 53°

✔ Check: 53 + 37 = 90 → Correct.

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Problem 4:

Angle XYZ is part of a straight line? Wait — look at point Y.
There’s angle XYW = 42°, and angle WYZ = 101°. But wait — those two angles are NOT on a straight line. Actually, angle XYZ is the big angle from X to Z passing through Y.

Wait — actually, looking again: points X, Y, Z — angle XYZ is the angle between rays YX and YZ.
But in the diagram, ray YW is between them. So:

m∠XYZ = m∠XYW + m∠WYZ = 42° + 101° = 143°

✔ Check: 42 + 101 = 143 → Correct.

*(Note: Sometimes diagrams show reflex angles, but here since both angles are drawn inside and adding up makes sense, we go with 143°.)*

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Problem 5:

At point D, we have angle GDE = 128°, and angle FDE = 86°.
We want angle FDG — which is the difference between them.

Because angle GDE is made of angle FDG + angle FDE.

So:
m∠FDG + 86° = 128°
→ m∠FDG = 128° - 86° = 42°

✔ Check: 42 + 86 = 128 → Correct.

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Problem 6:

At point R, angle SRU = 62°, and angle SRT = 17°.
We want angle TRU — which is the rest of the angle after removing 17° from 62°.

So:
m∠TRU = 62° - 17° = 45°

✔ Check: 17 + 45 = 62 → Correct.

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Final Answer:
1) 33°
2) 119°
3) 53°
4) 143°
5) 42°
6) 45°