Math Problem Statement
The measure of the complement of an angle excites it by 23' . Find the angle
Solution
Let's denote the measure of the angle as . The complement of an angle is what remains when the angle is subtracted from .
The problem states that the complement of the angle exceeds the angle by (minutes). So we can write this relationship as:
Step-by-step solution:
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Start by setting up the equation based on the given relationship:
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Add to both sides of the equation to get rid of the negative on the left-hand side:
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Subtract from both sides:
Since is in minutes, let's convert into degrees and minutes. , so:
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Now we have:
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Divide both sides by 2 to solve for :
Perform the division:
So, the measure of the angle is approximately .
Would you like further details or explanations?
Related Questions:
- What is the difference between complementary and supplementary angles?
- How would the equation change if the complement exceeds the angle by a different amount?
- What happens when the angle and its complement are equal?
- How can angles be measured in radians instead of degrees?
- How do we convert minutes and seconds of an angle into decimal degrees?
Tip: Always ensure that the units (degrees and minutes) are consistent throughout your calculations.
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Math Problem Analysis
Mathematical Concepts
Complementary Angles
Angle Measurement
Algebra
Formulas
Complement of an angle = 90° - angle
Basic Algebraic Equations
Theorems
Complementary Angles Theorem
Suitable Grade Level
Grades 7-10
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