Answer:
[tex]m\angle S=119^\circ[/tex], [tex]m\angle U=87^\circ[/tex]
Step-by-step explanation:
Since [tex]STUVW \sim HIJFG[/tex], we know that
[tex]m\angle S=m\angle H[/tex] and [tex]m\angle U=m\angle J[/tex]
since corresponding angles in similar triangles are equal in measure.
Therefore, looking at the second diagram, we see
[tex]m\angle H=119^\circ[/tex] and [tex]m\angle J=87^\circ[/tex].
Plugging these values into the equations we found in the first step, we get
[tex]m\angle S=m\angle H=119^\circ[/tex] and [tex]m\angle U=m\angle J=87^\circ.[/tex]
So, we have [tex]\boxed{m\angle S=119^\circ}[/tex] and [tex]\boxed{m\angle U=87^\circ}[/tex].
