Math Problem Statement
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:
-
86°, 53°, 41°
Sum = 86° + 53° + 41° = 180° → Yes, this forms a triangle. -
47°, 84°, 56°
Sum = 47° + 84° + 56° = 187° → No, this does not form a triangle. -
70°, 22°, 68°
Sum = 70° + 22° + 68° = 160° → No, this does not form a triangle. -
54°, 97°, 29°
Sum = 54° + 97° + 29° = 180° → Yes, this forms a triangle. -
33°, 90°, 57°
Sum = 33° + 90° + 57° = 180° → Yes, this forms a triangle. -
28°, 64°, 100°
Sum = 28° + 64° + 100° = 192° → No, this does not form a triangle. -
11°, 101°, 60°
Sum = 11° + 101° + 60° = 172° → No, this does not form a triangle. -
94°, 35°, 51°
Sum = 94° + 35° + 51° = 180° → Yes, this forms a triangle. -
52°, 83°, 45°
Sum = 52° + 83° + 45° = 180° → Yes, this forms a triangle. -
65°, 78°, 37°
Sum = 65° + 78° + 37° = 180° → Yes, this forms a triangle.
Summary:
- Yes
- No
- No
- Yes
- Yes
- No
- No
- Yes
- Yes
- Yes
Let me know if you need any clarifications or further details!
Here are some related questions for practice:
- What is the sum of the internal angles of a quadrilateral?
- Can a triangle have angles greater than 90°?
- What type of triangle is formed when all angles are less than 90°?
- How do you classify a triangle with one angle equal to 90°?
- What are the properties of an equilateral triangle?
Tip: For any polygon, the sum of interior angles can be found by the formula: , where 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