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][br][*]Find the relationship between two angles that have the same variable.[br][*]Use the Same-Side Interior Angles Theorem.[br][*]Use substitution and solve for [math]x[/math].[br][*]Find [math]m \angle 1[/math] and [math]m \angle 2[/math] using substitution.[br][*]Find the relationship between one of the known angles and the last unknown angle, [math] \angle 3[/math].[br][*]Use the Alternate Interior Angles Theorem.[br][*]Use the definition of congruence and substitution to find [math]m \angle 3[/math].[br][*]Use substitution to solve for [math]y[/math].[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit www.walch.com for more information.[br]