Learn why the sum of angles in a triangle is 180 degrees and practice exercises.
Master the 180° sum of angles in a triangle theorem. Practice solving multi-step geometry exercises with triangles and parallel line rules.
Frequently Asked Questions
Why do the angles of a triangle always add up to 180°?
This is one of the most elegant proofs in geometry. If you draw a line through the top vertex of any triangle that is parallel to its base, the three angles on that line (using the Z-rule for alternate interior angles) turn out to be exactly the three angles of the triangle — and they form a straight line, which is always 180°. This works for every triangle, no exceptions.
What are the Z, F, and X angle rules on parallel lines?
These are simple letter-based memory aids used when a transversal cuts parallel lines. The Z-rule denotes alternate interior angles (always equal), the F-rule denotes corresponding angles (always equal), and the X-rule denotes vertically opposite angles (always equal).