Constructing Angles

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I am a high school student, while solving the 'construction' chapter of my textbook I realized that it is not possible to construct every angle using a compass and a straight edge. why is it not possible to construct every angle using a compass(collapsible) and a straight edge?For example,i observed that it is not possible to construct an angle of 40 degree. how can i determine whether an angle is constructible using a compass(collapsible) and a straight edge or not?