Problem Overview:
The task involves finding the
complementary and
supplementary angles for given angles. Let's break it down step by step.
#### Definitions:
1.
Complementary Angles: Two angles are complementary if their measures add up to
90°.
- If one angle is \( x \), its complement is \( 90^\circ - x \).
2.
Supplementary Angles: Two angles are supplementary if their measures add up to
180°.
- If one angle is \( x \), its supplement is \( 180^\circ - x \).
#### Task:
- Find the complement of each angle in parts
a, b, c.
- Find the supplement of each angle in parts
e, f.
---
Solution:
#### Part a: Complement of \( 48^\circ \)
- The complement of an angle \( x \) is \( 90^\circ - x \).
- For \( 48^\circ \):
\[
\text{Complement} = 90^\circ - 48^\circ = 42^\circ
\]
#### Part b: Complement of \( 21^\circ \)
- For \( 21^\circ \):
\[
\text{Complement} = 90^\circ - 21^\circ = 69^\circ
\]
#### Part c: Complement of \( 44^\circ \)
- For \( 44^\circ \):
\[
\text{Complement} = 90^\circ - 44^\circ = 46^\circ
\]
#### Part e: Supplement of \( 159^\circ \)
- The supplement of an angle \( x \) is \( 180^\circ - x \).
- For \( 159^\circ \):
\[
\text{Supplement} = 180^\circ - 159^\circ = 21^\circ
\]
#### Part f: Supplement of \( 97^\circ \)
- For \( 97^\circ \):
\[
\text{Supplement} = 180^\circ - 97^\circ = 83^\circ
\]
---
Final Answers:
\[
\boxed{
\begin{aligned}
&\text{a. } 42^\circ \\
&\text{b. } 69^\circ \\
&\text{c. } 46^\circ \\
&\text{e. } 21^\circ \\
&\text{f. } 83^\circ
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of geometry complementary and supplementary angles worksheet.
