Let’s solve each problem step by step.
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Problem 1:
Triangle ABC is a right triangle (angle A = 90°). Angle B = 22°. We need to find angle C = x.
Sum of angles in any triangle = 180°
So, 90° + 22° + x = 180°
→ 112° + x = 180°
→ x = 180° - 112° =
68°
✔ Check: 90 + 22 + 68 = 180 → Correct.
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Problem 2:
All three sides have tick marks → this is an equilateral triangle. All angles are equal.
Each angle = 180° ÷ 3 =
60°
So x =
60°
✔ Check: 60 + 60 + 60 = 180 → Correct.
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Problem 3:
Two sides have tick marks → isosceles triangle. Base angles are equal.
Angle at A = 55° → so angle at C = 55° too.
Sum of angles = 180°
So, 55° + 55° + x = 180°
→ 110° + x = 180°
→ x = 70°
✔ Check: 55 + 55 + 70 = 180 → Correct.
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Problem 4:
We’re given two angles: 52° and 68°. Find x.
Sum = 180°
So, 52° + 68° + x = 180°
→ 120° + x = 180°
→ x = 60°
✔ Check: 52 + 68 + 60 = 180 → Correct.
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Problem 5:
Right triangle (angle A = 90°), angle B = 43°. Find angle C = x.
90° + 43° + x = 180°
→ 133° + x = 180°
→ x = 47°
✔ Check: 90 + 43 + 47 = 180 → Correct.
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Problem 6:
Given angles: 74° and 52°. Find x.
74° + 52° + x = 180°
→ 126° + x = 180°
→ x = 54°
✔ Check: 74 + 52 + 54 = 180 → Correct.
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Problem 7:
Given angles: 82° and 22°. Find x.
82° + 22° + x = 180°
→ 104° + x = 180°
→ x = 76°
✔ Check: 82 + 22 + 76 = 180 → Correct.
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Problem 8:
Right triangle (angle A = 90°), angle C = 64°. Find angle B = x.
90° + 64° + x = 180°
→ 154° + x = 180°
→ x = 26°
✔ Check: 90 + 64 + 26 = 180 → Correct.
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Problem 9:
Given angles: 54° and 49°. Find x.
54° + 49° + x = 180°
→ 103° + x = 180°
→ x = 77°
✔ Check: 54 + 49 + 77 = 180 → Correct.
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Final Answers:
1. x = 68°
2. x = 60°
3. x = 70°
4. x = 60°
5. x = 47°
6. x = 54°
7. x = 76°
8. x = 26°
9. x = 77°
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Final Answer:
1. 68°
2. 60°
3. 70°
4. 60°
5. 47°
6. 54°
7. 76°
8. 26°
9. 77°
Parent Tip: Review the logic above to help your child master the concept of triangle measurements worksheet.
