Mathematics

Both angles are inscribed angles subtending the same arc $AB$ from the same side of the chord. The key insight is that an inscribed angle's measure depends only on the arc it intercepts, not on where the vertex sits along the arc on the same side. Since $C$ and $D$ both "see" arc $AB$ from identical positions relative to the circle, they measure the same angle.

Both angles are inscribed angles subtending the same arc $AB$ from the same side of the chord. The key insight is that an inscribed angle's measure depends only on the arc it intercepts, not on where the vertex sits along the arc on the same side. Since $C$ and $D$ both "see" arc $AB$ from identical positions relative to the circle, they measure the same angle.