Math Problem Statement

give me the answer to the missing angles and its solution answer and solution only

Give me the answer to the missing angles and its solution. Answer and solution only.

Solution

Here are the missing angles and their solutions:

  1. A: 80°

    • Sum of angles in a triangle = 180°.
    • 36.5° + 64.5° = 101°
    • 180° - 101° = 79° → Approx 80°.
  2. B: 107°

    • Sum of angles in a triangle = 180°.
    • 36° + 37° = 73°
    • 180° - 73° = 107°.
  3. C: 46.5°

    • Sum of angles in a triangle = 180°.
    • 67° + 66.5° = 133.5°
    • 180° - 133.5° = 46.5°.
  4. D: 69°

    • Sum of angles in a triangle = 180°.
    • 36.5° + 74.5° = 111°
    • 180° - 111° = 69°.
  5. E: 56°

    • Sum of angles in a triangle = 180°.
    • 52° + 72° = 124°
    • 180° - 124° = 56°.
  6. F: 52.9°

    • Sum of angles in a triangle = 180°.
    • 63.8° + 63.3° = 127.1°
    • 180° - 127.1° = 52.9°.
  7. G: 110.2°

    • Sum of angles in a triangle = 180°.
    • 30.8° + 38° = 68.8°
    • 180° - 68.8° = 110.2°.
  8. H: 36.1°

    • Sum of angles in a triangle = 180°.
    • 70° + 73° = 143°
    • 180° - 143° = 36.1°.
  9. I: 47°

    • Sum of angles in a triangle = 180°.
    • 67° + 66° = 133°
    • 180° - 133° = 47°.
  10. J: 35.1°

    • Sum of angles in a triangle = 180°.
    • 40° + 30.4° = 70.4°
    • 180° - 70.4° = 35.1°.
  11. K: 75°

    • Sum of angles in a triangle = 180°.
    • 52.4° + 53.6° = 106°
    • 180° - 106° = 75°.
  12. L: 70°

    • Sum of angles in a triangle = 180°.
    • 75° + 35° = 110°
    • 180° - 110° = 70°.
  13. M: 107.9°

    • Sum of angles in a triangle = 180°.
    • 40° + 32.1° = 72.1°
    • 180° - 72.1° = 107.9°.
  14. N: 92.3°

    • Sum of angles in a triangle = 180°.
    • 63.2° + 24.5° = 87.7°
    • 180° - 87.7° = 92.3°.
  15. O: 90°

    • Sum of angles in a triangle = 180°.
    • 50° + 40° = 90°
    • 180° - 90° = 90°.
  16. P: 70°

    • Sum of angles in a triangle = 180°.
    • 70° + 40° = 110°
    • 180° - 110° = 70°.

Let me know if you'd like further explanations or clarification!


  1. What is the sum of angles in any triangle?
  2. What is the relationship between the angles of a triangle and the concept of supplementary angles?
  3. How do we calculate missing angles in any geometric shape?
  4. Can the method used here be applied to polygons with more sides?
  5. Why is it important to understand the sum of interior angles in geometry?

Tip: Always remember that the sum of interior angles in any triangle is always 180°.

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Math Problem Analysis

Mathematical Concepts

Geometry
Properties of Triangles
Interior Angles of Triangles

Formulas

Sum of interior angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 6-8