we know that
The sum of the internal angles in the triangle must be [tex]180[/tex] degrees
see the attached figure with letters to better understand the problem
Step [tex]1[/tex]
Find the measure of the angle x
In the triangle ABC
[tex]63\°+36\°+x\°=180\°[/tex]
solve for x
[tex]99\°+x\°=180\°[/tex]
[tex]x\°=180\°-99\°[/tex]
[tex]x=81\°[/tex]
therefore
the answer Part a) is
the measure of angle x is [tex]81\°[/tex]
Step [tex]2[/tex]
Find the measure of the angle z
we know that
[tex]x+z=180\°[/tex] --------> by supplementary angles
substitute the value of x
[tex]81\°+z=180\°[/tex]
[tex]z=180\°-81\°[/tex]
[tex]z=99\°[/tex]
therefore
the answer Part b) is
the measure of angle z is [tex]99\°[/tex]
Step [tex]3[/tex]
Find the measure of the angle y
In the triangle ACD
[tex]13\°+z\°+y\°=180\°[/tex]
solve for y
[tex]13\°+99\°+y\°=180\°[/tex]
[tex]112\°+y\°=180\°[/tex]
[tex]y\°=180\°-112\°[/tex]
[tex]y\°=68\°[/tex]
therefore
the answer Part c) is
the measure of angle y is [tex]68\°[/tex]
