Part 1) ![x=28.75\°](/tpl/images/0182/4827/dfa47.png)
Part 2) ![z=44.5\°](/tpl/images/0182/4827/2d8cd.png)
Part 3) ![y=135.5\°](/tpl/images/0182/4827/95ac4.png)
Step-by-step explanation:
Part 1) Determine the value of x
we know that
------> by corresponding angles
Solve for x
Multiply by 5 both sides to remove the fraction
![5(\frac{6}{5}x+10)\°=5(2x-13)\°](/tpl/images/0182/4827/272c9.png)
![6x+50=10x-65](/tpl/images/0182/4827/915b3.png)
![10x-6x=50+65](/tpl/images/0182/4827/4cc91.png)
![4x=115](/tpl/images/0182/4827/e7448.png)
Divide by 4 both sides
![x=28.75\°](/tpl/images/0182/4827/dfa47.png)
Part 2) Determine the value of z
we know that
------> by corresponding angles
we have
![x=28.75\°](/tpl/images/0182/4827/dfa47.png)
substitute the value of x and solve for z
![z=(\frac{6}{5}(28.75)+10)=44.5\°](/tpl/images/0182/4827/76dfe.png)
Part 3) Determine the value of y
we know that
------> by supplementary angles
we have
![z=44.5\°](/tpl/images/0182/4827/2d8cd.png)
substitute and solve for y
![y+44.5\°=180\°](/tpl/images/0182/4827/d56d0.png)
![y=180\°-44.5\°=135.5\°](/tpl/images/0182/4827/ebebc.png)