If sec(4x - 50°) = cosec(50° - x), then the value of x is?

Answer: Option C

$$\begin{array}{rl}& \text{sec}\left(4x-{50}^{\circ }\right)=\text{cosec}\left({50}^{\circ }-x\right)\\ & \text{sec}\left(4x-{50}^{\circ }\right)=\text{cosec}\left({90}^{\circ }-\left({40}^{\circ }+x\right)\right)\\ & \text{sec}\left(4x-{50}^{\circ }\right)=\text{sec}\left({40}^{\circ }+x\right)\\ & 4x-50^{\circ }=40^{\circ }+x\\ & 3x=90^{\circ }\\ & x=30^{\circ }\end{array}$$