The construction of angles in general is a classical problem in mathematics. The early mathematicians failed to redress the problem under the stated restrictions because they did not have a bearing to approach the problem from. Eventually, the classical problem was assumed impossible. This paper contributes the interest in solving this crucial problem by presenting a very straight forward methodology of constructing angles in general. Several geometrical constructions were carried out to answer the questions; what methodology would generalize the construction of all angles measurable using the protractor? What approach would lead to the construction of some regular polygons whose the angle subtended at their center would only be estimated? The methods revealed in this work responded to these two questions in a simple but a more fashionable way. Two smart chords were generated which helped construct any angle a multiple of both five or two, and both five and two. The methodology involved relating the angles at a difference of ten degrees from each other in their descending order. The idea yielded excellent results. Linear simultaneous equations were used to confirm the accuracy of the two developed chords. The chords were therefore considered to form the base for constructing angles in general.