A mathematical framework is provided for shape-from-angle problems, and four primitive problems based on it are discussed. For three of them, algebraic equations are provided from a geometric analysis. A generic 1-D algorithm is proposed for designing a 1-D search algorithm, usable for any shape-from-angle problems. By designing the problem-dependent parts of the generic algorithm, specific 1-D search algorithms are constructed for each problem. The generic algorithm finds all the feasible configurations by detecting the zero-crossing points of a problem-dependent test function on a constraint curve. Experimental results show the effectiveness of each specific algorithm and the applicability of the generic algorithm to several types of shape-from-angle problems.