angle-chase-in-figure
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.
How to solve
- 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)
Tool fingerprint (1–17)
Grade distribution
- Gr 4 1
- Gr 5 1
- Gr 7 2
- Gr 8 1