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Pattern Anatomy

Each pattern, deconstructed.

angle-chase-in-figure

Rank 25/25 0.2% of all AMC problems Grade 4–8

An unknown angle in a plane figure is recovered by propagating a small set of angle facts from the angles that are given: a straight line is 180 degrees, a triangle's angles sum to 180, a quadrilateral's to 360, angles about a point sum to 360, vertical angles are equal, and equal sides or equal radii force equal base angles. No coordinates, lengths, or areas are needed - the figure's incidence structure alone carries the deduction, and the work is choosing an order of steps in which each new angle follows from ones already known.

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27-year frequency
1999–2026
2026 forecast slots

How to solve

Primary tools see-draworganize
What to look for
  • Move the given measure one triangle further from the target to lengthen the chase without changing any fact used
  • Replace a printed measure with an equal-sides tick mark so the solver must supply the isosceles step themselves
  • Underdetermine the individual angles but keep a grouped sum determined, so the solver must chase chunks rather than single angles

Sub-archetype mix (3)

Click a row to see member problems.

  • straight-and-triangle-sum-chase 20% (1)

    The chase runs purely on the 180-degree facts - angles on a line, the angle sum of a triangle, and (by triangulation) of a polygon - stepping from the given measures through adjacent triangles until the target angle is reached.

  • isosceles-equal-angle-chase 40% (2)

    Equal sides, equal radii, or a bisected angle force two angles to be equal; naming that repeated angle once and chasing it through the figure is what closes the deduction. Often the individual angles are not determined but the doubled or grouped quantity is.

  • fixed-instrument-angle-composition 40% (2)

    The given angles are not printed but come from an object with known fixed angles - a 30-60-90 or 45-45-90 set square, or the hands of a clock at a stated time - and the target is an angle formed where two such objects overlap or where the hands land.

More data (year-over-year, tool fingerprint, grade distribution, all members)
5
members
1999–2026
Active years
Year-over-year

Tool fingerprint (1–17)

Grade distribution

  • Gr 4
    1
  • Gr 5
    1
  • Gr 7
    2
  • Gr 8
    1