What Is Angle Chasing?

Angle chasing is a popular method of solving problems in geometry that employs various properties of, and identities that include angles.

Angles are basic elements in many geometric situations; there are inscribed, secant, complementary, vertical, supplementary angles.

Equal angles emerge as

It's worth remembering that

Acute angles in a right triangle are complementary; they add up to 90°.
Angles formed by a straight line and a ray emanating from one of its points are supplementary; they add up to 180°.
The sum of angles in a (plane) triangle is always 180°.
Central angles in a circle are twice as large as the inscribed angles subtend by the same arc.
The angles at the base of an isosceles triangle are equal. (Thales' Theorem>)
A tangent to a circle is perpendicular to the radius at the point of tangency.
The Exterior Angle Theorem: an angle exterior to a triangle equals the sum of two enterior and opposite angles.
Inscribed and secant angles are nicely expressed interms of subtending arcs.
And, of course, All right angles are equal.

Here is an incomplete list of problems at this site where angle chasing plays a major role in the solution:

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