Complementary, Supplementary, Vertical Angle Worksheets - Free Printable

To solve the problem of finding the complementary angles in the given worksheet, we need to recall the definition of complementary angles:

Complementary Angles: Two angles are complementary if their measures add up to 90 degrees.

Step-by-Step Solution:

#### a.
- Given angle: \( \angle ASC = 23^\circ \)
- Complementary angle: \( 90^\circ - 23^\circ = 67^\circ \)

#### b.
- Given angle: \( \angle BGD = 55^\circ \)
- Complementary angle: \( 90^\circ - 55^\circ = 35^\circ \)

#### c.
- Given angle: \( \angle LJK = 72^\circ \)
- Complementary angle: \( 90^\circ - 72^\circ = 18^\circ \)

#### d.
- Given angle: \( \angle MNO = 44^\circ \)
- Complementary angle: \( 90^\circ - 44^\circ = 46^\circ \)

#### e.
- Given angle: \( \angle QRS = 70^\circ \)
- Complementary angle: \( 90^\circ - 70^\circ = 20^\circ \)

#### f.
- Given angle: \( \angle UVW = 54^\circ \)
- Complementary angle: \( 90^\circ - 54^\circ = 36^\circ \)

#### g.
- Given angle: \( \angle XYZ = 27^\circ \)
- Complementary angle: \( 90^\circ - 27^\circ = 63^\circ \)

#### h.
- Given angle: \( \angle DEF = 40^\circ \)
- Complementary angle: \( 90^\circ - 40^\circ = 50^\circ \)

#### i.
- Given angle: \( \angle GHI = 69^\circ \)
- Complementary angle: \( 90^\circ - 69^\circ = 21^\circ \)

#### j.
- Given angle: \( \angle LMN = 38^\circ \)
- Complementary angle: \( 90^\circ - 38^\circ = 52^\circ \)

#### k.
- Given angle: \( \angle EFG = 15^\circ \)
- Complementary angle: \( 90^\circ - 15^\circ = 75^\circ \)

#### l.
- Given angle: \( \angle VTU = 45^\circ \)
- Complementary angle: \( 90^\circ - 45^\circ = 45^\circ \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{a. } \angle ASC = 67^\circ & \text{b. } \angle BGD = 35^\circ \\
\text{c. } \angle LJK = 18^\circ & \text{d. } \angle MNO = 46^\circ \\
\text{e. } \angle QRS = 20^\circ & \text{f. } \angle UVW = 36^\circ \\
\text{g. } \angle XYZ = 63^\circ & \text{h. } \angle DEF = 50^\circ \\
\text{i. } \angle GHI = 21^\circ & \text{j. } \angle LMN = 52^\circ \\
\text{k. } \angle EFG = 75^\circ & \text{l. } \angle VTU = 45^\circ \\
\end{array}
}
\]

Each answer is derived by subtracting the given angle from 90 degrees, ensuring the sum of the angle and its complement equals 90 degrees.