Answer:
Part 1) The value of y is [tex]y=0.8[/tex]
Part 2) The value of z is [tex]z=0.9[/tex]
Part 3) The value of x is [tex]x=0.5[/tex]
Step-by-step explanation:
step 1
Find the value of y
we know that
[tex](\frac{225y}{2})\°=90\°[/tex] ----> given problem (is a right angle)
[tex]y=90(2)/225[/tex]
[tex]y=0.8[/tex]
step 2
Find the value of z
we know that
[tex](50z+13)\°=(80z-14)\°[/tex] ----> by vertical angles
Solve for z
[tex]80z-50z=13+14[/tex]
[tex]30z=27[/tex]
[tex]z=27/30[/tex]
[tex]z=0.9[/tex]
step 3
Find the value of x
we know that
[tex](44x+125y)\°+(80z-14)\°=180\°[/tex] ----> by supplementary angles (linear pair)
Substitute the value of y and the value of z and solve for x
[tex](44x+125(0.8))\°+(80(0.9)-14)\°=180\°[/tex]
[tex](44x+100)\°+(72-14)\°=180\°[/tex]
[tex]44x+158=180[/tex]
[tex]44x=180-158[/tex]
[tex]44x=22[/tex]
[tex]x=0.5[/tex]
