In this paper we shall present results related to trigonometric approximation of functions belonging to the weighted generalized Lipschitz class by the $(C^{1} \cdot T)$ matrix means of their Fourier series. The results of Lal in \cite{Lal} will be extended to a more general summability method. Moreover, we present the results on degree of approximation to conjugates of functions belonging to a weighted generalized Lipschitz class by the $(C^{1} \cdot T)$ matrix means of their conjugate Fourier series.