∠110 and ∠x are corresponding angles, therefore:
[tex]m\angle x=110[/tex]
The exterior angle is equal to the sum of the two opposite interior angles, therefore:
[tex]\begin{gathered} 40+m\angle y=m\angle x \\ 40+m\angle y=110 \\ solve_{\text{ }}for_{\text{ }}m\angle y\colon \\ m\angle y=110-40 \\ m\angle y=70 \end{gathered}[/tex]
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the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. therefore:
[tex]\begin{gathered} 15+20=35 \\ 35>x \end{gathered}[/tex]
where x is the missing side, besides:
[tex]x>0[/tex]
so:
[tex]0
