In the following diagram, [math]\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}[/math] and [math]\overleftrightarrow{AC} \parallel \overleftrightarrow{BD}[/math]. If [math]m \angle 1 = 3(x + 15)[/math], [math]m \angle 2 = 2x + 55[/math], and [math]m \angle 3 = 4y + 9[/math], find the measures of the unknown angles and the values of [math]x[/math] and [math]y[/math].
[list=1] [*]Find the relationship between two angles that have the same variable. [*]Use the Same-Side Interior Angles Theorem. [*]Use substitution and solve for [math]x[/math]. [*]Find [math]m \angle 1[/math] and [math]m \angle 2[/math] using substitution. [*]Find the relationship between one of the known angles and the last unknown angle, [math] \angle 3[/math]. [*]Use the Alternate Interior Angles Theorem. [*]Use the definition of congruence and substitution to find [math]m \angle 3[/math]. [*]Use substitution to solve for [math]y[/math]. [/list]