Math Problem Statement

  1. 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 xx.

  • The complement of an angle is 90x90^\circ - x.
  • The supplement of an angle is 180x180^\circ - x.

According to the problem, the sum of the complement and supplement is two more than twice the angle, which gives us the equation:

(90x)+(180x)=2x+2(90^\circ - x) + (180^\circ - x) = 2x + 2

Step-by-step solution:

  1. Simplify the left-hand side of the equation: 90+1802x=2x+290 + 180 - 2x = 2x + 2 2702x=2x+2270 - 2x = 2x + 2

  2. Move all terms involving xx to one side: 2702=2x+2x270 - 2 = 2x + 2x 268=4x268 = 4x

  3. Solve for xx: x=2684=67x = \frac{268}{4} = 67^\circ

Step 4: Find the complement of the angle

The complement of the angle is: 9067=2390^\circ - 67^\circ = 23^\circ

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:

  1. What is the supplement of an angle if its complement is known?
  2. Can an angle have both a complement and a supplement simultaneously?
  3. What happens when an angle exceeds 9090^\circ in terms of complement and supplement?
  4. How can we visualize the relationship between complement and supplement geometrically?
  5. Can this approach be generalized to angles in radians?

Tip: Always remember that the sum of complementary angles is 9090^\circ, while the sum of supplementary angles is 180180^\circ.

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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