Question

Please help me really quick pleasee answer choices: a)2 b)11 c)20 d)29

Answer 1

Answer:

C. $x=20^{\circ}$

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

$m\angle 6=45^{\circ}$

Angle 6 and angle with measure $5x+35^{\circ}$ are the same side interior angles when two parallel lines are cut by transversal. The same side interior angles add up to 180°, then

$m\angle 6+5x+35^{\circ}=180^{\circ}\\ \\45^{\circ}+5x+35^{\circ}=180^{\circ}\\ \\5x=180^{\circ}-45^{\circ}-35^{\circ}\\ \\5x=100^{\circ}\\ \\x=20^{\circ}$