Math Problem Statement

if supplementary of angle is 4 times its compliment then the angle is?

Solution

Let the angle be denoted by xx.

Step 1: Definitions

  • Complementary angles add up to 9090^\circ, so the complement of xx is 90x90^\circ - x.
  • Supplementary angles add up to 180180^\circ, so the supplement of xx is 180x180^\circ - x.

Step 2: Equation Setup

According to the problem, the supplementary angle is 4 times the complementary angle. Therefore, we can set up the equation: 180x=4(90x)180^\circ - x = 4(90^\circ - x)

Step 3: Solve the Equation

  1. Distribute the 4 on the right side: 180x=3604x180^\circ - x = 360^\circ - 4x
  2. Move all terms involving xx to one side: 3x=3601803x = 360^\circ - 180^\circ 3x=1803x = 180^\circ
  3. Solve for xx: x=1803=60x = \frac{180^\circ}{3} = 60^\circ

Thus, the angle is 60\boxed{60^\circ}.

Do you have any questions or would you like more details?

Here are 5 related questions:

  1. What is the complement of a 6060^\circ angle?
  2. How do you calculate the supplement of a given angle?
  3. If the angle were 4545^\circ, how would its complement and supplement relate?
  4. What happens if an angle is greater than 9090^\circ? Can it have a complement?
  5. Can two angles be both complementary and supplementary?

Tip: To check if your calculation is correct, add the angle's complement and supplement to see if they add up to 90° and 180°, respectively.

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Math Problem Analysis

Mathematical Concepts

Complementary Angles
Supplementary Angles
Linear Equations

Formulas

Complementary angles: x + (90° - x) = 90°
Supplementary angles: x + (180° - x) = 180°
Equation: 180° - x = 4(90° - x)

Theorems

Angle Sum Theorems
Basic Properties of Complementary and Supplementary Angles

Suitable Grade Level

Grade 7-8