Lines, Angles, and Triangles
Every angle figure runs on a short list of rules: straight lines hold 180 degrees, right angles hold 90, X crossings hold equal pairs, and triangles sum to 180. The points leak in the rule, a supplement computed as a complement or vertical angles summed, in the ratio, similar triangles paired by position instead of by angle or scaled by the flipped fraction, and at the end, in the report: the solved variable bubbled when the question asked for the angle built from it.
These patterns aren't really about whether you can subtract from 180. They're about whether the relationship got named before the arithmetic ran, whether the proportion kept matched sides and a consistent direction, and whether the number you reported is the measure the question actually asked for.
The work
4 ways in · any order
Lesson
Lines, Angles, and Triangles
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Name the relationship (straight line, right angle, X crossing) before computing, run triangle and exterior-angle sums, build similarity ratios from matched sides, and substitute back for the angle asked. The lesson works the method and the three patterns that derail it, and it saves the trap for last: the solved variable standing in for the angle.
Diagnostic
10-item topic check
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Ten items across the three patterns: the wrong angle rule fired, similarity ratios flipped or mismatched, and the variable or the wrong angle reported. A mix of angle chases, triangle sums, shadow proportions, and solve-then-substitute. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.