The smallest positive value of $x$ (in degrees) for which $\tan ( x+100 ^{\circ}$$)=\tan (x+50^{\circ}) \times \tan x \times \tan (x-50^{\circ})$

Question

$(a)\;60^{\large\circ}\qquad(b)\;90^{\large\circ}\qquad(c)\;45^{\large\circ}\qquad(d)\;30^{\large\circ}$