The wave fronts of a light wave travelling in vacuum are given by x + y + z = c. The angle made by the direction of propagation of light with the X-axis is

Ray is perpendicular to wave front thus, the vector along ray is same as a vector perpendicular
to wave front x+y+z. Thus, the vector along the ray is $\widehat{\mathrm{i}}+\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$ , let ray makes α with x-axis
$\begin{array}{l}\cos \mathrm{\alpha }=\frac{1}{\sqrt{1^2+1^2+1^2}}\\ \Rightarrow \cos \mathrm{\alpha }=\frac{1}{\sqrt{3}}\Rightarrow \mathrm{\alpha }={\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)\end{array}$