Math Problem Statement
- The sum of the complement and supplement of a certain angle is two more than twice the said angle, What is the complement of the angle?
Solution
Let the angle be denoted as .
- The complement of an angle is .
- The supplement of an angle is .
According to the problem, the sum of the complement and supplement is two more than twice the angle, which gives us the equation:
Step-by-step solution:
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Simplify the left-hand side of the equation:
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Move all terms involving to one side:
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Solve for :
Step 4: Find the complement of the angle
The complement of the angle is:
Thus, the complement of the angle is 23 degrees.
Would you like further clarification or details on this? Here are some related questions you could explore:
- What is the supplement of an angle if its complement is known?
- Can an angle have both a complement and a supplement simultaneously?
- What happens when an angle exceeds in terms of complement and supplement?
- How can we visualize the relationship between complement and supplement geometrically?
- Can this approach be generalized to angles in radians?
Tip: Always remember that the sum of complementary angles is , while the sum of supplementary angles is .
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Math Problem Analysis
Mathematical Concepts
Complementary Angles
Supplementary Angles
Algebra
Formulas
Complement of an angle: 90° - x
Supplement of an angle: 180° - x
Equation: (90° - x) + (180° - x) = 2x + 2
Theorems
Sum of Complementary Angles (90°)
Sum of Supplementary Angles (180°)
Suitable Grade Level
Grades 8-10
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