Question
4. Analyze and Persevere Find the measure of the complement to an \( 18^{\circ} \) angle. Explain your answer.
Ask by Perkins Rodriquez. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The complement of a \( 18^{\circ} \) angle is \( 72^{\circ} \).
Solution
To find the measure of the complement of an \( 18^{\circ} \) angle, we need to understand the concept of complementary angles. Two angles are considered complementary if the sum of their measures is \( 90^{\circ} \).
### Step-by-step solution:
1. **Identify the known angle**: We have an angle \( A = 18^{\circ} \).
2. **Set up the equation for complementary angles**: Let \( C \) be the measure of the complement of angle \( A \). According to the definition of complementary angles, we can write the equation:
\[
A + C = 90^{\circ}
\]
3. **Substitute the known value**: Substitute \( A = 18^{\circ} \) into the equation:
\[
18^{\circ} + C = 90^{\circ}
\]
4. **Solve for \( C \)**: To find \( C \), we can rearrange the equation:
\[
C = 90^{\circ} - 18^{\circ}
\]
5. **Perform the calculation**:
\[
C = 72^{\circ}
\]
### Conclusion:
The measure of the complement to an \( 18^{\circ} \) angle is \( 72^{\circ} \). This means that when you add \( 18^{\circ} \) and \( 72^{\circ} \), the total is \( 90^{\circ} \), confirming that they are complementary angles.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the measure of the complement of an \( 18^{\circ} \) angle, you subtract \( 18^{\circ} \) from \( 90^{\circ} \) because complementary angles add up to \( 90^{\circ} \). So, \( 90^{\circ} - 18^{\circ} = 72^{\circ} \). Therefore, the complement of an \( 18^{\circ} \) angle is \( 72^{\circ} \). Understanding complementary angles is essential in various fields, especially in geometry and trigonometry. In architecture, for instance, knowing how to calculate complementary angles can assist in designing structures that involve right angles, helping ensure stability and aesthetic appeal. This concept is also used in carpentry to create perfect corners in furniture or framing.
