Answer:
C. [tex]x=20^{\circ}[/tex]
Step-by-step explanation:
Angle 6 and angle with measure 45° are vertical angles (opposite angles whan two lines intersect). By Vertical Angles Theorem, vertical angles are congruent, so
[tex]m\angle 6=45^{\circ}[/tex]
Angle 6 and angle with measure [tex]5x+35^{\circ}[/tex] are the same side interior angles when two parallel lines are cut by transversal. The same side interior angles add up to 180°, then
[tex]m\angle 6+5x+35^{\circ}=180^{\circ}\\ \\45^{\circ}+5x+35^{\circ}=180^{\circ}\\ \\5x=180^{\circ}-45^{\circ}-35^{\circ}\\ \\5x=100^{\circ}\\ \\x=20^{\circ}[/tex]
