[tex]z = 29°[/tex]
Step-by-step explanation:
According to the triangle angle sum theorem, the sum of the interior angles of a triangle is 180°. So for [tex]\triangle{ABD},[/tex] the sum of its interior angles is
[tex]43 + 59 + x = 180[/tex]
[tex]\Rightarrow x = 78°[/tex]
But [tex]\angle{x}[/tex] is supplementary with [tex]\angle{y}[/tex] so that
[tex]x + y = 180 \Rightarrow y = 180 - 78 = 102°[/tex]
Now that we know the value of y, we apply the triangle angle sum theorem to [tex]\triangle{BDC}[/tex] and we get
[tex]49 + y + z = 180 \Rightarrow 49 + 102 + z = 180[/tex]
Solving for z, we finally get
[tex]z = 29°[/tex]
