Find the value of x that makes m ∥ n

20

Step-by-step explanation:

Theorem:

If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.

Lines m and n are cut by a transversal.

Angles 3x and 2x + 20 are alternate interior angles.

For lines m and n to be parallel, angles 3x and 2x + 20 must be congruent, so their measures must be equal.

3x = 2x + 20

x = 20

20

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)