Math Problem Statement

Three times the measure of an angle is 15 less than the measure of its complement.

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."

  1. Let the measure of the angle be xx.

  2. 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 90x90 - x.

  3. The equation based on the problem is: 3x=(90x)153x = (90 - x) - 15 This says that "three times the angle xx" equals "the complement 90x90 - x" minus 15.

Solving the equation:

3x=90x153x = 90 - x - 15 3x=75x3x = 75 - x Now, add xx to both sides to move all the xx's to one side: 3x+x=753x + x = 75 4x=754x = 75 Now, divide both sides by 4: x=754=18.75x = \frac{75}{4} = 18.75

So, the measure of the angle is 18.75°.

To find the complement, subtract this from 90: 9018.75=71.25°90 - 18.75 = 71.25°

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:

  1. What is the complement of an angle of 30°?
  2. How do you solve for angles that are supplementary (adding up to 180°)?
  3. Can two angles be complementary if one is obtuse?
  4. If an angle is half of its complement, how do you set up the equation to solve it?
  5. 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