Answer: [tex]\angle x=29\°[/tex]
Step-by-step explanation:
By definition, the alternate interior angles formed when a transversal intersects two parallel lines, are congruent, which means that their measures are equal.
Notice in the figure attached that the angle 42° and the angle "y" are Alternate Interior Angles. Therefore:
[tex]y=42\°[/tex]
You can identify that the angles "y", "x" and 109° are supplementary angles, which means that their sum is 180°.
Knowing this, you can write the following equation:
[tex]42\°+109\°+x=180\°[/tex]
Finally, solving for "x", you get that its measure is:
[tex]42\°+109\°+x=180\°\\\\x=180\°-151\°\\\\x=29\°[/tex]
