SAT Math formula sheet · all 24 · Geometry and Trigonometry · #19 of 24

Angle relationships on the SAT: How It Is Tested

Lines, angles, and triangles

Angle Relationships diagram for the SAT: When they say parallel, you are using one of the parallel-line relationships: alternate interior, alternate exterior, co
What it is really testingWhen they say parallel, you are using one of the parallel-line relationships: alternate interior, alternate exterior, corresponding, or same-side interior angles. The other relationships shown here do not require parallel lines and are always true: vertical angles, linear pair, and triangle sum.

The question from the sheet

Medium
SAT Geometry and Trigonometryanswer B
tmnx°y°z°Note: Figure not drawn to scale.In the figure, lines mm and nn are parallel. If x=10k−11x = 10k - 11 and y=8k+15y = 8k + 15, what is the value of zz?
A180180
✓6161
C119119
D1313

How the diagram applies

  1. xx and yy are vertical angles, so they are equal: 10k−11=8k+1510k - 11 = 8k + 15, giving k=13k = 13 and x=y=119x = y = 119.
  2. yy and zz are same-side interior angles, so they ADD to 180180. They are not equal.
  3. z=180−119=61z = 180 - 119 = 61.

Answer: B

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Common Questions

It comes up as an SAT lines, angles, and triangles question. When they say parallel, you are using one of the parallel-line relationships: alternate interior, alternate exterior, corresponding, or same-side interior angles. The other relationships shown here do not require parallel lines and are always true: vertical angles, linear pair, and triangle sum.

x and y are vertical angles, so they are equal: 10k - 11 = 8k + 15, giving k = 13 and x = y = 119. y and z are same-side interior angles, so they ADD to 180. They are not equal. z = 180 - 119 = 61.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Angle Relationships is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.