Answer:
Part 1) [tex]x=28.75\°[/tex]
Part 2) [tex]z=44.5\°[/tex]
Part 3) [tex]y=135.5\°[/tex]
Step-by-step explanation:
Part 1) Determine the value of x
we know that
[tex](\frac{6}{5}x+10)\°=(2x-13)\°[/tex] ------> by corresponding angles
Solve for x
Multiply by 5 both sides to remove the fraction
[tex]5(\frac{6}{5}x+10)\°=5(2x-13)\°[/tex]
[tex]6x+50=10x-65[/tex]
[tex]10x-6x=50+65[/tex]
[tex]4x=115[/tex]
Divide by 4 both sides
[tex]x=28.75\°[/tex]
Part 2) Determine the value of z
we know that
[tex]z=(\frac{6}{5}x+10)\°[/tex] ------> by corresponding angles
we have
[tex]x=28.75\°[/tex]
substitute the value of x and solve for z
[tex]z=(\frac{6}{5}(28.75)+10)=44.5\°[/tex]
Part 3) Determine the value of y
we know that
[tex]y+z=180\°[/tex] ------> by supplementary angles
we have
[tex]z=44.5\°[/tex]
substitute and solve for y
[tex]y+44.5\°=180\°[/tex]
[tex]y=180\°-44.5\°=135.5\°[/tex]
