Using ruler and a pair of compasses only,
(a) construct :
(i) (Delta)XYZ such that |XY| = 10cm, < XYZ = 30° and < YXZ = 45°.
(ii) locus, (l_{1}), of points equidistant from Y and Z.
(iii) locus, (l_{2}), of points parallel to XY through Z.
(b) Locate M, the point of intersection of (l_{1}) and (l_{2}).
(c) Measure < ZMY.
Explanation
(a), (b)
(c) < ZMY = 120°.