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