(a) \(< ADB = < ACB = 20^\circ\) (Angle in the same segment). In \(\Delta ACY\), \(\hat{C} = < ACB\) (i) \(\hat{C} + \hat{A} + \hat{Y} = 180^\circ\) \(20^\circ + \hat{A} + 60^\circ = 180^\circ\) \(\hat{A} = 180^\circ - 80^\circ = 100^\circ\) \(< CAY = \hat{A} = 100^\circ\) \(< CAX = 180^\circ - 100^\circ = 80^\circ\) (ii) In \(\Delta ACB\), \(\hat{B} = \hat{C} = \frac{180^\circ - 20^\circ}{2} \) = \(\frac{160^\circ}{2}\) = \(80^\circ\) In \(\Delta ABY\), \(< ABY = \hat{B} = 180^\circ - 80^\circ\) = \(100^\circ\) (b) \((m + 1)(m - 3) \equiv m^{2} - km + c\) \(m^{2} - 3m + m - 3 = m^{2} - 2m - 3\) \(m^{2} - 2m - 3 \equiv m^{2} - km + c\) \(\implies k = 2 ; c = -3\)