Problem
GEO-B2-M01-P004 Opposite Angles
#4
★★☆☆☆ Level 2 of 5
Convex quadrilateral \(ABCD\) is cyclic. Prove that \(\angle BAD+\angle BCD=180^\circ\).
Both angles are related to arcs \(BD\).
Angle \(\angle BAD\) stands on the arc \(BD\) not containing \(A\), while \(\angle BCD\) stands on the other arc \(BD\). These two arcs together form the whole circle, so the corresponding inscribed angles sum to \(180^\circ\).
A simple problem, but it reinforces the relation between ordinary and oriented notation.