Let’s solve each triangle one by one. Remember:
the three angles inside any triangle always add up to 180°. We’ll use that rule for every problem.
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Problem 1:
Angles given: 70°, 45°, and x°
So: 70 + 45 + x = 180
→ 115 + x = 180
→ x = 180 - 115 =
65
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Problem 2:
Angles given: 82°, 35°, and x°
So: 82 + 35 + x = 180
→ 117 + x = 180
→ x = 180 - 117 =
63
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Problem 3:
Angles given: 58°, 86°, and x°
So: 58 + 86 + x = 180
→ 144 + x = 180
→ x = 180 - 144 =
36
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Problem 4:
This one has an exterior angle (x°) next to the triangle. The two interior angles are 61° and 52°.
First, find the third interior angle:
61 + 52 = 113 → so missing interior angle = 180 - 113 = 67°
Now, x° is on a straight line with that 67° angle → they add to 180°
So: x = 180 - 67 =
113
*(Alternatively, you can remember: exterior angle = sum of the two opposite interior angles → 61 + 52 = 113 — same answer!)*
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Problem 5:
We have angles: x°, y°, 50° inside the triangle. Also, there’s an exterior angle of 120° next to y°.
Since y° and 120° are on a straight line:
y = 180 - 120 =
60
Now, inside the triangle: x + y + 50 = 180
→ x + 60 + 50 = 180
→ x + 110 = 180
→ x =
70
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Problem 6:
Angles given: 77°, 64°, and x°
So: 77 + 64 + x = 180
→ 141 + x = 180
→ x = 180 - 141 =
39
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Problem 7:
Angles given: 13°, 29°, and x°
So: 13 + 29 + x = 180
→ 42 + x = 180
→ x = 180 - 42 =
138
Wait — that seems too big? Let me double-check:
13 + 29 = 42 → 180 - 42 = 138. Yes, it’s correct. It’s an obtuse triangle.
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Problem 8:
Inside the triangle: 64°, 38°, and q°
So: 64 + 38 + q = 180
→ 102 + q = 180
→ q = 78
Now, x° is on a straight line with q° → x + q = 180
→ x + 78 = 180
→ x =
102
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Problem 9:
Inside the triangle: 81°, 69°, and y°
So: 81 + 69 + y = 180
→ 150 + y = 180
→ y =
30
Now, x° is on a straight line with the 69° angle → x + 69 = 180
→ x =
111
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Problem 10:
Right triangle! One angle is 90°, another is 45°, and x°
So: 90 + 45 + x = 180
→ 135 + x = 180
→ x =
45
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Problem 11:
Angles given: 35°, 15°, and x°
So: 35 + 15 + x = 180
→ 50 + x = 180
→ x =
130
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Problem 12:
Right triangle again! One angle is 90°, another is 45°, and x°
Same as Problem 10: 90 + 45 + x = 180
→ x =
45
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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
Parent Tip: Review the logic above to help your child master the concept of finding missing angles in triangles worksheet.
