The angle made by the line joining the points $(2,0)$ and $( - 4,2\sqrt 3 )$ with x axis is -

Angle made by the line joining the points

$\left( { { 2 },{ 0} } \right) \, \, and\, \, \left( { -{ 4 },2{ { \sqrt { 3 } } } } \right)$ with $x$ axis.

Slope of line

$m=\dfrac { { \Delta y } }{ { \Delta x } }$

$=\dfrac { { { y_{ 2 } }-{ y_{ 1 } } } }{ { { x_{ 2 } }-{ x_{ 1 } } } } =\dfrac { { 2\sqrt { 3 } -0 } }{ { -4-2 } }$

$=\dfrac { { 2\sqrt { 3 } } }{ { -6 } } =\dfrac { { \sqrt { 3 } } }{ { -\sqrt { 3 } \times \sqrt { 3 } } } =\dfrac { { -1 } }{ { \sqrt { 3 } } }$

$m=\tan \theta$

$\tan \theta =\dfrac { { -1 } }{ { \sqrt { 3 } } }$

$\theta =-{ \tan ^{ -1 } }\dfrac { 1 }{ { \sqrt { 3 } } } =150^{ \circ }.$