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

Let the angle be denoted by \( x \).

### Step 1: Definitions
- **Complementary angles** add up to \( 90^\circ \), so the complement of \( x \) is \( 90^\circ - x \).
- **Supplementary angles** add up to \( 180^\circ \), so the supplement of \( x \) is \( 180^\circ - x \).

### Step 2: Equation Setup
According to the problem, the supplementary angle is 4 times the complementary angle. Therefore, we can set up the equation:
\[
180^\circ - x = 4(90^\circ - x)
\]

### Step 3: Solve the Equation
1. Distribute the 4 on the right side:
   \[
   180^\circ - x = 360^\circ - 4x
   \]
2. Move all terms involving \( x \) to one side:
   \[
   3x = 360^\circ - 180^\circ
   \]
   \[
   3x = 180^\circ
   \]
3. Solve for \( x \):
   \[
   x = \frac{180^\circ}{3} = 60^\circ
   \]

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

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

Here are 5 related questions:
1. What is the complement of a \( 60^\circ \) angle?
2. How do you calculate the supplement of a given angle?
3. If the angle were \( 45^\circ \), how would its complement and supplement relate?
4. What happens if an angle is greater than \( 90^\circ \)? 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.

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

Learn how to solve the problem where the supplementary angle is 4 times its complement. This step-by-step guide involves understanding complementary and supplementary angles, setting up a linear equation, and solving for the angle. Suitable for Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation