Math Problem Statement

State whether the given set of angles form a triangle.

Solution

To determine whether each set of angles forms a triangle, we need to check if the sum of the three angles is equal to 180°.

Let's go through the questions step-by-step:

  1. 86°, 53°, 41°
    Sum = 86° + 53° + 41° = 180° → Yes, this forms a triangle.

  2. 47°, 84°, 56°
    Sum = 47° + 84° + 56° = 187° → No, this does not form a triangle.

  3. 70°, 22°, 68°
    Sum = 70° + 22° + 68° = 160° → No, this does not form a triangle.

  4. 54°, 97°, 29°
    Sum = 54° + 97° + 29° = 180° → Yes, this forms a triangle.

  5. 33°, 90°, 57°
    Sum = 33° + 90° + 57° = 180° → Yes, this forms a triangle.

  6. 28°, 64°, 100°
    Sum = 28° + 64° + 100° = 192° → No, this does not form a triangle.

  7. 11°, 101°, 60°
    Sum = 11° + 101° + 60° = 172° → No, this does not form a triangle.

  8. 94°, 35°, 51°
    Sum = 94° + 35° + 51° = 180° → Yes, this forms a triangle.

  9. 52°, 83°, 45°
    Sum = 52° + 83° + 45° = 180° → Yes, this forms a triangle.

  10. 65°, 78°, 37°
    Sum = 65° + 78° + 37° = 180° → Yes, this forms a triangle.

Summary:

  1. Yes
  2. No
  3. No
  4. Yes
  5. Yes
  6. No
  7. No
  8. Yes
  9. Yes
  10. Yes

Let me know if you need any clarifications or further details!


Here are some related questions for practice:

  1. What is the sum of the internal angles of a quadrilateral?
  2. Can a triangle have angles greater than 90°?
  3. What type of triangle is formed when all angles are less than 90°?
  4. How do you classify a triangle with one angle equal to 90°?
  5. What are the properties of an equilateral triangle?

Tip: For any polygon, the sum of interior angles can be found by the formula: (n2)×180°(n - 2) \times 180°, where nn is the number of sides.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angles

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 5-7