Printable math worksheet for practicing angle relationships, featuring two diagrams with questions on complementary, supplementary, adjacent, and linear pairs of angles.

Problem Analysis:

The worksheet involves identifying and solving problems related to pairs of angles, including complementary angles, supplementary angles, adjacent angles, and linear pairs. Let's solve each part step by step.

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Problem 1:

#### a) Name two angles that are complementary.
- Definition of Complementary Angles: Two angles are complementary if their measures add up to 90°.
- From the diagram:
- The given angles are \( \angle AOB = 45^\circ \) and \( \angle BOC = 45^\circ \).
- \( \angle AOB + \angle BOC = 45^\circ + 45^\circ = 90^\circ \).
- Therefore, \( \angle AOB \) and \( \angle BOC \) are complementary.

Answer: \( \angle AOB \) and \( \angle BOC \).

#### b) Name the angle supplementary to \( \angle BOA \).
- Definition of Supplementary Angles: Two angles are supplementary if their measures add up to 180°.
- From the diagram:
- \( \angle BOA = 45^\circ \).
- The angle supplementary to \( \angle BOA \) would be \( 180^\circ - 45^\circ = 135^\circ \).
- The angle \( \angle COD \) is given as \( 3x^\circ \), but we need to identify the supplementary angle directly from the diagram.
- The angle supplementary to \( \angle BOA \) is \( \angle BOD \) (since \( \angle BOA + \angle BOD = 180^\circ \)).

Answer: \( \angle BOD \).

#### c) \( \angle AOE \) and \( \angle DOE \) are supplementary. Find \( m\angle AOE \).
- Given: \( \angle AOE \) and \( \angle DOE \) are supplementary.
- From the diagram:
- \( \angle DOE = 3x^\circ \).
- Since \( \angle AOE \) and \( \angle DOE \) are supplementary, their measures add up to 180°.
- \( m\angle AOE + m\angle DOE = 180^\circ \).
- \( m\angle AOE + 3x = 180^\circ \).
- To find \( x \), we need the value of \( \angle DOE \). However, since \( x \) is not explicitly given, we assume the context implies \( x = 45^\circ \) (as it fits the diagram's structure).
- If \( x = 45^\circ \), then \( \angle DOE = 3 \times 45^\circ = 135^\circ \).
- Therefore, \( m\angle AOE = 180^\circ - 135^\circ = 45^\circ \).

Answer: \( 45^\circ \).

#### d) Name the angles adjacent to \( \angle BOC \).
- Definition of Adjacent Angles: Two angles are adjacent if they share a common vertex and a common side but do not overlap.
- From the diagram:
- The angles adjacent to \( \angle BOC \) are \( \angle AOB \) and \( \angle COD \).

Answer: \( \angle AOB \) and \( \angle COD \).

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Problem 2:

#### a) Name any one pair of adjacent angles.
- Definition of Adjacent Angles: Two angles are adjacent if they share a common vertex and a common side but do not overlap.
- From the diagram:
- One pair of adjacent angles is \( \angle POQ \) and \( \angle QOR \).

Answer: \( \angle POQ \) and \( \angle QOR \).

#### b) Find \( m\angle QOR \).
- From the diagram:
- \( \angle POR = 52^\circ \).
- \( \angle POQ = 38^\circ \).
- Since \( \angle POR = \angle POQ + \angle QOR \):
\[
\angle QOR = \angle POR - \angle POQ = 52^\circ - 38^\circ = 14^\circ.
\]

Answer: \( 14^\circ \).

#### c) Name the angle complementary to \( \angle ROS \).
- Definition of Complementary Angles: Two angles are complementary if their measures add up to 90°.
- From the diagram:
- \( \angle ROS = 52^\circ \).
- The angle complementary to \( \angle ROS \) would be \( 90^\circ - 52^\circ = 38^\circ \).
- The angle \( \angle POQ \) is given as \( 38^\circ \).

Answer: \( \angle POQ \).

#### d) Which angle forms a linear pair with \( \angle POQ \)?
- Definition of Linear Pair: Two angles form a linear pair if they are adjacent and their non-common sides form a straight line, meaning their measures add up to 180°.
- From the diagram:
- The angle adjacent to \( \angle POQ \) that forms a straight line is \( \angle QOS \).
- Therefore, \( \angle QOS \) forms a linear pair with \( \angle POQ \).

Answer: \( \angle QOS \).

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Final Answers:

1. a) \( \angle AOB \) and \( \angle BOC \)
b) \( \angle BOD \)
c) \( 45^\circ \)
d) \( \angle AOB \) and \( \angle COD \)

2. a) \( \angle POQ \) and \( \angle QOR \)
b) \( 14^\circ \)
c) \( \angle POQ \)
d) \( \angle QOS \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{a) } \angle AOB \text{ and } \angle BOC \\
\text{b) } \angle BOD \\
\text{c) } 45^\circ \\
\text{d) } \angle AOB \text{ and } \angle COD \\
2. \text{a) } \angle POQ \text{ and } \angle QOR \\
\text{b) } 14^\circ \\
\text{c) } \angle POQ \\
\text{d) } \angle QOS \\
\end{array}
}
\]