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(D) Let the angles the line makes with the positive directions of the $x$,$y$,and $z$-axes be $\alpha, \beta$,and $\gamma$ respectively.Given that $\a

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$90$

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(D) Let the angles the line makes with the positive directions of the $x$,$y$,and $z$-axes be $\alpha, \beta$,and $\gamma$ respectively.Given that $\alpha = 45^\circ$ and $\beta = 45^\circ$.Let the direction cosines of the line be $l, m, n$.Then $l = \cos \alpha = \cos 45^\circ = \frac{1}{\sqrt{2}}$,$m = \cos \beta = \cos 45^\circ = \frac{1}{\sqrt{2}}$,$n = \cos \gamma$.We know that $l^2 + m^2 + n^2 = 1$.Substituting the values,we get $(\frac{1}{\sqrt{2}})^2 + (\frac{1}{\sqrt{2}})^2 + \cos^2 \gamma = 1$.$\frac{1}{2} + \frac{1}{2} + \cos^2 \gamma = 1$.$1 + \cos^2 \gamma = 1$.$\cos^2 \gamma = 0$.$\cos \gamma = 0$.Therefore,$\gamma = 90^\circ$.

If a line makes an angle of $45^\circ$ with the positive directions of each of $x$-axis and $y$-axis,then the angle that the line makes with the positive direction of the $z$-axis is .............. $^\circ$.

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