Once you know a few angle facts — vertical angles, angles on a line, and the parallel-line angles — you can chase an unknown angle across a figure: each known angle unlocks the next, step by step, until you reach the one you want. This page is about doing that — first by watching one worked chase, then by solving fresh ones yourself.

Watch one chase

Two parallel lines (note the matching arrows) are cut by a transversal. We are told one angle is 65^\circ. Step through to see how that single fact forces two more.

The marks of the trade

A good angle-chase diagram is covered in marks that record what you know: ticks for equal lengths, arcs for equal angles, a small square for a right angle (and the matching arrows for parallel lines you saw above). Here is an isosceles triangle with its altitude — the two equal sides are ticked, the two equal base angles are arced, and the square marks where the altitude meets the base at a right angle.

Solve one yourself

Here is a freshly generated chase. Some angles are given; the highlighted box is the one to find, with a step or two of theorem in between. Type each unknown angle, use the tools to mark parallels or draw a helper line if it aids your thinking, then press Check. Hit Refresh for a brand-new figure — the problems are built only from the theorems taught in the lessons leading here.