1. Problem (i): Find the measure of \(\angle BOD\) in figure (ii).\nGiven vertical angles at intersection O, \(\angle BOD\) is opposite to the given \(80^\circ\) angle \(\angle AOC\).\nVertical angles are equal, so \(\angle BOD = 80^\circ\).\nAnswer: (c) 80º.\n\n2. Problem (ii): Find the measure of \(\angle y\) in figure (ii).\nThe question states \(\angle y\) between points A and C is \(80^\circ\) in the figure given, but options differ.\nVertical angles and supplementary angles add to \(180^\circ\).\nSince \(\angle y + 80^\circ=180^\circ\), we get \(\angle y = 100^\circ\).\nAnswer: (d) 100º.\n\n3. Problem (iii): Find the measure of \(\angle 1\) in figure (i) where \(AB \parallel EF \parallel CD\).\nGiven angles: \(108^\circ\) at A and \(112^\circ\) at C. These are alternate interior or exterior angles with respect to the parallel lines.\nSum of interior angles on the same side of transversal equals 180º.\nCalculate \(\angle 1\) using \(\angle 1 + 108^\circ = 180^\circ\) gives \(\angle 1 = 72^\circ\).\nAnswer: (b) 72º.\n\n4. Problem (iv): Find the measure of \(2x\) in figure (i).\nGiven angles adjacent to \(x\) are 108º and 112º and lines are parallel. Since \(2x\) is external or supplementary angle of internal angles,\nSum angles around point equal 360º: \(108^\circ + 112^\circ + 2x = 360^\circ\).\nCalculate \(2x = 360^\circ - (108^\circ + 112^\circ) = 140^\circ\).\nAnswer: (a) 140º.