Answer: [tex]z=24\°[/tex]
Step-by-step explanation:
We need to find the measure of "x":
Based on the figure, we know that:
[tex]48\°+x+x=180\°[/tex]
Then, we need to solve for "x". Therefore, its measure in degrees is:
[tex]48\°+2x=180\°\\\\2x=180\°-48\°\\\\2x=132\°\\\\x=\frac{132\°}{2}\\\\x=66\°[/tex]
By definition, the sum of the interior angles of a triangle is 180 degrees. Since we know the measure of "x" and we know that one of the interior angles is a the right angle (an angle that measures 90 degrees), we can conclude that:
[tex]z+90\°+x=180\°[/tex]
Substituting the value of "x" into the equation and solving for "z", we get:
[tex]z+90\°+66\°=180\°\\\\z=24\°[/tex]
