Before you read

Answer first — see what you already know.

Two parallel railroad tracks are crossed by a road (transversal). A pair of alternate interior angles are $(3 x + 10) °$ and $(5 x - 20) °$ . Find $x$ .

A
5
B
10
C
15
D
20

Check your answer

Answer:

Before you read

Answer first — see what you already know.

In a building's framework, two parallel beams are cut by a diagonal brace. The co-interior angles are $(2 x + 30) °$ and $(4 x) °$ . Find $x$ .

A
15
B
20
C
25
D
30

Check your answer

Answer:

Theory

Angle Pairs with Parallel Lines

When a transversal crosses two parallel lines, it creates 8 angles with special relationships:

Parallel lines cut by a transversal

Corresponding angles: Same position at each intersection $\to$ Equal

Alternate interior angles: Opposite sides of transversal, between parallels $\to$ Equal

Alternate exterior angles: Opposite sides, outside parallels $\to$ Equal

Co-interior (same-side interior) angles: Same side, between parallels $\to$ Supplementary (sum to $180°$ )

Example 1

Lines $l \parallel m$ are cut by a transversal. One angle is $65°$ . Find all 8 angles.

The 4 angles equal to $65°$ : corresponding and vertical angles

The 4 angles equal to $115°$ : supplementary to $65°$

Four angles of

65°

and four of

115°

Strategy

SAT Pro Tip

If the SAT tells you lines are parallel, immediately look for corresponding or alternate interior angles — they're equal. If it asks you to PROVE lines are parallel, show that corresponding angles are equal or alternate interior angles are equal.

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