Pairs of Angles Worksheets - Free Printable

To solve the problems involving pairs of angles, we need to use properties such as supplementary angles, complementary angles, vertical angles, and corresponding angles. Let's go through each problem step by step.

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Problem 1:

#### Image (I)
- Given: \( m\angle UXV = ? \)
- Diagram: Two angles are shown as supplementary angles (they form a straight line).
- Solution:
- The two angles are supplementary, meaning their measures add up to \(180^\circ\).
- One angle is given as \(125^\circ\).
- Therefore, \( m\angle UXV = 180^\circ - 125^\circ = 55^\circ \).

#### Image (II)
- Given: \( m\angle FJQ = ? \)
- Diagram: Two angles are shown as complementary angles (they form a right angle).
- Solution:
- The two angles are complementary, meaning their measures add up to \(90^\circ\).
- One angle is given as \(37^\circ\).
- Therefore, \( m\angle FJQ = 90^\circ - 37^\circ = 53^\circ \).

#### Image (III)
- Given: \( m\angle LON = ? \)
- Diagram: Two angles are shown as vertical angles.
- Solution:
- Vertical angles are congruent, meaning they have the same measure.
- One angle is given as \(48^\circ\).
- Therefore, \( m\angle LON = 48^\circ \).

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Problem 2:

#### Image (IV)
- Given: \( m\angle MNL = ? \)
- Diagram: Two angles are shown as supplementary angles.
- Solution:
- The two angles are supplementary, meaning their measures add up to \(180^\circ\).
- One angle is given as \(110^\circ\).
- Therefore, \( m\angle MNL = 180^\circ - 110^\circ = 70^\circ \).

#### Image (V)
- Given: \( m\angle HTW = ? \)
- Diagram: Two angles are shown as complementary angles.
- Solution:
- The two angles are complementary, meaning their measures add up to \(90^\circ\).
- One angle is given as \(45^\circ\).
- Therefore, \( m\angle HTW = 90^\circ - 45^\circ = 45^\circ \).

#### Image (VI)
- Given: \( m\angle CRB = ? \)
- Diagram: Two angles are shown as vertical angles.
- Solution:
- Vertical angles are congruent, meaning they have the same measure.
- One angle is given as \(60^\circ\).
- Therefore, \( m\angle CRB = 60^\circ \).

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Problem 3:

#### Image (VII)
- Given: \( m\angle CYE = ? \)
- Diagram: Two angles are shown as supplementary angles.
- Solution:
- The two angles are supplementary, meaning their measures add up to \(180^\circ\).
- One angle is given as \(100^\circ\).
- Therefore, \( m\angle CYE = 180^\circ - 100^\circ = 80^\circ \).

#### Image (VIII)
- Given: \( m\angle STC = ? \)
- Diagram: Two angles are shown as complementary angles.
- Solution:
- The two angles are complementary, meaning their measures add up to \(90^\circ\).
- One angle is given as \(30^\circ\).
- Therefore, \( m\angle STC = 90^\circ - 30^\circ = 60^\circ \).

#### Image (IX)
- Given: \( m\angle ZRB = ? \)
- Diagram: Two angles are shown as vertical angles.
- Solution:
- Vertical angles are congruent, meaning they have the same measure.
- One angle is given as \(50^\circ\).
- Therefore, \( m\angle ZRB = 50^\circ \).

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Final Answers:

1. \( m\angle UXV = 55^\circ \)
2. \( m\angle FJQ = 53^\circ \)
3. \( m\angle LON = 48^\circ \)
4. \( m\angle MNL = 70^\circ \)
5. \( m\angle HTW = 45^\circ \)
6. \( m\angle CRB = 60^\circ \)
7. \( m\angle CYE = 80^\circ \)
8. \( m\angle STC = 60^\circ \)
9. \( m\angle ZRB = 50^\circ \)

\[
\boxed{
\begin{array}{ll}
m\angle UXV = 55^\circ & m\angle FJQ = 53^\circ \\
m\angle LON = 48^\circ & m\angle MNL = 70^\circ \\
m\angle HTW = 45^\circ & m\angle CRB = 60^\circ \\
m\angle CYE = 80^\circ & m\angle STC = 60^\circ \\
m\angle ZRB = 50^\circ &
\end{array}
}
\]