Math Problem Statement
Solution
To solve the problem:
Definitions and Setup
Let:
- = the smallest angle.
- = the angle that is three times the smallest.
- = the largest angle, which is five times the smallest.
Complementary Rule
The sum of the three angles is . Hence, we set up the equation:
Simplification
Solve for
Values of the Angles
- Smallest angle:
- Second angle:
- Largest angle:
Final Answer
The three angles are , , and .
Let me know if you want further details or additional explanations. Here are 5 related questions to expand your understanding:
- What is the definition of complementary angles?
- How do you solve similar problems with more unknown variables?
- Can complementary angles involve more than three angles?
- What happens if one of the angles is expressed as a fraction of another?
- How does this change if the total sum were (supplementary angles)?
Tip: Always check the sum of your angles to ensure the calculations align with the given conditions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Complementary Angles
Formulas
Sum of complementary angles: x + 3x + 5x = 90
Theorems
Definition of complementary angles
Suitable Grade Level
Grades 6-8
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