Calculating Angles on Parallel Lines with Transversals (A ... - Free Printable

Problem: Calculate the missing angles and provide a reason for each answer.

#### Section A

1. Angle \( a \):
- Diagram: Two parallel lines with a transversal. One angle is given as \( 48^\circ \).
- Reasoning: The angle \( a \) is an alternate interior angle to the given \( 48^\circ \) angle. Alternate interior angles are equal when the lines are parallel.
- Answer: \( a = 48^\circ \)
- Reason: Alternate Interior Angles

2. Angle \( b \):
- Diagram: Two parallel lines with a transversal. One angle is given as \( 52^\circ \).
- Reasoning: The angle \( b \) is a corresponding angle to the given \( 52^\circ \) angle. Corresponding angles are equal when the lines are parallel.
- Answer: \( b = 52^\circ \)
- Reason: Corresponding Angles

3. Angle \( c \):
- Diagram: Two parallel lines with a transversal. One angle is given as \( 65^\circ \).
- Reasoning: The angle \( c \) is a co-interior (or consecutive interior) angle to the given \( 65^\circ \) angle. Co-interior angles add up to \( 180^\circ \) when the lines are parallel.
- Answer: \( c = 180^\circ - 65^\circ = 115^\circ \)
- Reason: Co-Interior Angles Sum to \( 180^\circ \)

4. Angle \( d \):
- Diagram: Two parallel lines with a transversal. One angle is given as \( 71^\circ \).
- Reasoning: The angle \( d \) is an alternate exterior angle to the given \( 71^\circ \) angle. Alternate exterior angles are equal when the lines are parallel.
- Answer: \( d = 71^\circ \)
- Reason: Alternate Exterior Angles

#### Section B

1. Angle \( a \):
- Diagram: Two parallel lines with a transversal. One angle is given as \( 108^\circ \).
- Reasoning: The angle \( a \) is a corresponding angle to the given \( 108^\circ \) angle. Corresponding angles are equal when the lines are parallel.
- Answer: \( a = 108^\circ \)
- Reason: Corresponding Angles

2. Angle \( b \):
- Diagram: Two parallel lines with a transversal. One angle is given as \( 43^\circ \).
- Reasoning: The angle \( b \) is an alternate interior angle to the given \( 43^\circ \) angle. Alternate interior angles are equal when the lines are parallel.
- Answer: \( b = 43^\circ \)
- Reason: Alternate Interior Angles

3. Angle \( c \):
- Diagram: Two intersecting lines. One angle is given as \( 114^\circ \).
- Reasoning: The angle \( c \) is a vertically opposite angle to the given \( 114^\circ \) angle. Vertically opposite angles are equal.
- Answer: \( c = 114^\circ \)
- Reason: Vertically Opposite Angles

4. Angle \( d \):
- Diagram: Two intersecting lines. One angle is given as \( 79^\circ \).
- Reasoning: The angle \( d \) is a supplementary angle to the given \( 79^\circ \) angle. Supplementary angles add up to \( 180^\circ \).
- Answer: \( d = 180^\circ - 79^\circ = 101^\circ \)
- Reason: Supplementary Angles

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Angle } a: & 48^\circ, \text{Alternate Interior Angles} \\
\text{Angle } b: & 52^\circ, \text{Corresponding Angles} \\
\text{Angle } c: & 115^\circ, \text{Co-Interior Angles Sum to } 180^\circ \\
\text{Angle } d: & 71^\circ, \text{Alternate Exterior Angles} \\
\text{Angle } a: & 108^\circ, \text{Corresponding Angles} \\
\text{Angle } b: & 43^\circ, \text{Alternate Interior Angles} \\
\text{Angle } c: & 114^\circ, \text{Vertically Opposite Angles} \\
\text{Angle } d: & 101^\circ, \text{Supplementary Angles}
\end{array}
}
\]