Angle Relationships on the SAT
Vertical, Linear, and Parallel
Build equations from context, spot patterns fast, and practice with intent.
Why the SAT Emphasizes Angle Relationships
Angle relationship questions are SAT favorites because a few rules unlock a lot of problems. When you can spot vertical angles, linear pairs, and angle sums, the algebra becomes quick.
This lesson trains you to identify the relationship first, then write the equation. You will see which angles are equal, which add to $180^\circ$, and how to avoid mixing up adjacent and vertical angles.
A Simple Definition Unlocks Angle Relationships
Vertical angles are opposite each other and always equal. A linear pair forms a straight line and sums to $180^\circ$. These two facts appear in nearly every SAT angle diagram.
Once you identify the relationship, you translate it into an equation. The diagram gives you the structure, and the algebra gives you the value. The most common mistake is adding angles that are not actually related.
Work Through Angle Relationships Step by Step
A linear pair has angles $x$ and $35^\circ$. What is $x$?
Use a linear pair relationship to set up the equation and solve for the angle.
Linear pair sums to $180^\circ$
Solve for $x$ to isolate the variable.
Use Desmos to Check Angle Relationships
A linear pair has angles $x$ and $35^\circ$. What is $x$?
Desmos is not usually faster for angle relationships because the algebra is simple. It is best used only to verify arithmetic after you set up the relationship.
180 - 35
Most of the time, pure geometry is faster here.
Desmos is rarely faster here. Recognizing the angle relationships and writing a quick equation is almost always the fastest route.
Expert move: Treat Desmos as a quick arithmetic check after you set up the angle equation; the geometry relationship is the real work.
When to skip Desmos: If the relationship is clear (vertical, linear pair, corresponding), solve it on paper and move on.
- Desmos features used: quick arithmetic evaluation.
- Common mistake: mixing up corresponding and alternate interior angles.
Practice Angle Relationships with SAT-Style Questions
Identify the relationship, then solve.
Two vertical angles are formed by intersecting lines. One angle measures . What is the measure of its vertical angle?
Angles in a linear pair measure and . What is ?
Parallel lines are cut by a transversal. A corresponding angle is . What is the measure of the matching corresponding angle?
If two interior angles on the same side of a transversal are and , what is ?
Key Takeaways to Remember for Angle Relationships
- Vertical angles are equal, linear pairs sum to $180^\circ$.
- Corresponding angles are equal when lines are parallel.
- Most problems reduce to a one step equation.
