Answer:
[tex]5.\text{ Solution:}\\\\\text{Type of Angles: }\underline{\text{Right}}\\\\\text{Key Information: }\underline{\text{Equal to 90}}^\circ.\\\\\text{Equation: }2x+71^\circ=90^\circ \Rightarrow 2x=90^\circ-71^\circ=19^\circ\Rightarrow x=\bigg(\dfrac{19}{2}\bigg)^\circ\\\\\text{Solution: }x=\bigg(\dfrac{19}{2}\bigg)^\circ[/tex]
[tex]\text{6. Solution:}\\\\\text{Type of angles: \underline{Vertical}}\\\\\text{Key Information: \underline{Angles are congruent}}\\\\\text{Equation: }-2x-6^\circ=40^\circ\Rightarrow -2x=46^\circ\Rightarrow x=-23^\circ[/tex]
[tex]\text{Solution: }x=-23^\circ[/tex]