When a line (transversal) crosses two parallel lines, it creates pairs of angles with special relationships. The Digital SAT tests your ability to identify these relationships and use them to find unknown angles.
Core Concepts
Vertical Angles
When two lines cross, opposite angles are equal: and .
Also: (supplementary).
Parallel Lines and Transversals
When a transversal crosses parallel lines:
Corresponding angles (same position): equal.
Alternate interior angles (opposite sides, between parallels): equal.
Alternate exterior angles (opposite sides, outside parallels): equal.
Co-interior (same-side interior) angles (same side, between parallels): supplementary (sum to 180°).
Angle Sum Rules
- Angles on a straight line sum to .
- Angles at a point sum to .
- Interior angles of a triangle sum to .
Strategy Tips
Tip 1: Label the Parallel Lines
Mark parallel lines with arrows. Identify the transversal.
Tip 2: Look for Z, F, and C Shapes
- Z-shape: alternate angles (equal).
- F-shape: corresponding angles (equal).
- C-shape (or U-shape): co-interior angles (sum to 180°).
Tip 3: Use Multiple Steps
You may need to find one angle using vertical angles, then use that to find another via parallel line relationships.
Worked Example: Example 1
Lines and are parallel. A transversal makes a 65° angle with line . Find the alternate interior angle at line .
Alternate interior angles are equal: 65°.
Worked Example: Example 2
A transversal crosses two parallel lines. One angle is 110°. Find all eight angles.
The eight angles come in two groups: 110° and 70° (since ). Corresponding/alternate angles are equal; supplementary pairs sum to 180°.
Worked Example: SAT-Style
In the figure, lines and are parallel. If angle 1 = and angle 2 = (where they are alternate interior angles), find .
→ →
Angle = .
Worked Example: Example 4
Co-interior angles: one is and the other is . Find .
→ → →
Practice Problems
Problem 1
Two parallel lines cut by a transversal. One angle is 55°. Find the co-interior angle.
Problem 2
Corresponding angles: one is and the other is . Find .
Problem 3
Find all angles when a transversal makes a 72° angle with one of two parallel lines.
Want to check your answers and get step-by-step solutions?
Common Mistakes
- Confusing alternate and co-interior angles. Alternate = equal. Co-interior = supplementary.
- Forgetting that lines must be parallel for these rules to apply.
- Misidentifying which angles are corresponding. They must be in the same relative position.
Key Takeaways
Corresponding angles: equal (F-shape).
Alternate interior angles: equal (Z-shape).
Co-interior angles: supplementary, sum to 180° (C-shape).
Vertical angles: always equal.
These rules only apply when lines are parallel.