Math Problem Statement
if supplementary of angle is 4 times its compliment then the angle is?
Solution
Let the angle be denoted by .
Step 1: Definitions
- Complementary angles add up to , so the complement of is .
- Supplementary angles add up to , so the supplement of is .
Step 2: Equation Setup
According to the problem, the supplementary angle is 4 times the complementary angle. Therefore, we can set up the equation:
Step 3: Solve the Equation
- Distribute the 4 on the right side:
- Move all terms involving to one side:
- Solve for :
Thus, the angle is .
Do you have any questions or would you like more details?
Here are 5 related questions:
- What is the complement of a angle?
- How do you calculate the supplement of a given angle?
- If the angle were , how would its complement and supplement relate?
- What happens if an angle is greater than ? Can it have a complement?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Find the Measure of the Complement of an Angle with Supplement Exceeding by 9
Solve for Supplementary Angles: One Angle Four Times the Other
Solving for Two Supplementary Angles Where One is Four Times Greater
Angle whose supplement is twelve degrees more than twice its complement
Find Two Supplementary Angles When One is Twice the Other