Math Problem Statement
Solution
Let's break down the problem step by step and write an equation:
The problem says:
"Three times the measure of an angle is 15 less than the measure of its complement."
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Let the measure of the angle be .
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The complement of an angle is found by subtracting the angle from 90° because complementary angles add up to 90°. So, the measure of its complement will be .
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The equation based on the problem is: This says that "three times the angle " equals "the complement " minus 15.
Solving the equation:
Now, add to both sides to move all the 's to one side: Now, divide both sides by 4:
So, the measure of the angle is 18.75°.
To find the complement, subtract this from 90:
Thus, the angle is 18.75°, and its complement is 71.25°.
Would you like further details or have any questions about the solution? Here are a few related problems to consider:
- What is the complement of an angle of 30°?
- How do you solve for angles that are supplementary (adding up to 180°)?
- Can two angles be complementary if one is obtuse?
- If an angle is half of its complement, how do you set up the equation to solve it?
- What are the properties of complementary and supplementary angles?
Tip: Always double-check that your equation correctly represents the relationship described in the problem before solving.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Complementary Angles
Formulas
x + y = 90°
3x = (90 - x) - 15
Theorems
Complementary Angles Theorem
Suitable Grade Level
Grades 8-10
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