The measures of two vertically opposite angles are $(5x + 30^{\circ})$ and $(8x - 60^{\circ})$,then the value of $x = \dots$

Prove that a triangle must have at least two acute angles.

In the figure,if $AB \parallel CD$,$\angle BMX = 125^{\circ}$ and $\angle CNX = 55^{\circ}$,find $\angle MXN$. (in $^{\circ}$)

In the figure,if $OP \parallel RS,$ $\angle OPQ = 110^{\circ}$ and $\angle QRS = 130^{\circ},$ then $\angle PQR$ is equal to: (in $^{\circ}$)

$A$ transversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. Will the two lines always be parallel? Give reason for your answer.

$\angle X$ and $\angle Y$ are complementary angles. If $\angle X = 4 \angle Y$,then find $\angle X$ and $\angle Y$.