Geometry · Quadrilaterals · Congruent triangles · Isosceles triangle · Angle chasing
Let \(ABCD\) be a quadrilateral such that
\[ \angle BCA + \angle CAD = 180^{\circ} \qquad\text{and}\qquad AB = AD + BC. \]
Prove that \(\angle BAC + \angle ACD = \angle CDA\).
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Serbian Municipal Competition 2014, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source