Find the missing angles in triangles worksheet with 12 problems, each featuring a triangle with two known angles and one unknown angle to solve.

Let’s solve each triangle problem step by step.

Remember:
→ The sum of all angles inside a triangle is always 180°.
→ If an angle is outside the triangle (like in problems 4, 5, 8, 9, 12), it forms a straight line with the inside angle — so they add up to 180° too.

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Problem 1:
Angles: 70°, 45°, x°
x = 180 - 70 - 45 = 65°

Problem 2:
Angles: 82°, 35°, x°
x = 180 - 82 - 35 = 63°

Problem 3:
Angles: 58°, 86°, x°
x = 180 - 58 - 86 = 36°

Problem 4:
Inside angles: 61°, 52° → missing inside angle = 180 - 61 - 52 = 67°
But x° is the *outside* angle next to that 67° → x = 180 - 67 = 113°

Problem 5:
Top right angle is 120° outside → inside angle = 180 - 120 = 60°
Now we have inside angles: 50°, 60°, and y° → y = 180 - 50 - 60 = 70°
Then x° is the third angle? Wait — no, looking again:
Actually, the triangle has angles: x°, y°, and 50°. And y° + 120° = 180° → y = 60°
So x = 180 - 50 - 60 = 70°

Wait — let me recheck diagram 5:
It shows a triangle with one vertex having an exterior angle of 120°, so the interior angle at that corner is 60°.
The other two interior angles are x° and 50°.
So: x + 50 + 60 = 180 → x = 70°
And y° is the same as the 60°? No — wait, label says “y°” at the top right, which is adjacent to 120° → so y = 180 - 120 = 60°
But then x is the left angle → x = 180 - 50 - 60 = 70°

Actually, looking again — maybe y is the interior angle? Yes, because it’s drawn inside the triangle at that corner. So:

Interior angles: x°, y°, 50°
Exterior at y’s corner is 120° → so y = 180 - 120 = 60°
Then x = 180 - 50 - 60 = 70°

So for problem 5:
x = 70°, y = 60°

But the question only asks for missing angles — probably both x and y. Let’s list both.

Problem 6:
Angles: x°, 77°, 64°
x = 180 - 77 - 64 = 39°

Problem 7:
Angles: x°, 13°, 29°
x = 180 - 13 - 29 = 138°

Problem 8:
Inside angles: 64°, 38°, q° → q = 180 - 64 - 38 = 78°
x° is outside at q’s corner → x = 180 - 78 = 102°

Problem 9:
Inside angles: 81°, 69°, y° → y = 180 - 81 - 69 = 30°
x° is outside at the 69° corner → x = 180 - 69 = 111°

Problem 10:
Right triangle: 90°, 45°, x°
x = 180 - 90 - 45 = 45°

Problem 11:
Angles: 35°, 15°, x°
x = 180 - 35 - 15 = 130°

Problem 12:
Right triangle: 90°, 45°, x°
x = 180 - 90 - 45 = 45°

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Now, compiling all answers clearly:

1. x = 65°
2. x = 63°
3. x = 36°
4. x = 113°
5. x = 70°, y = 60°
6. x = 39°
7. x = 138°
8. x = 102°, q = 78°
9. x = 111°, y = 30°
10. x = 45°
11. x = 130°
12. x = 45°

Final Answer:
1. 65°
2. 63°
3. 36°
4. 113°
5. x=70°, y=60°
6. 39°
7. 138°
8. x=102°, q=78°
9. x=111°, y=30°
10. 45°
11. 130°
12. 45°