Answer:
y, because Triangle RST is similar to triangle VUT
Step-by-step explanation:
The complete question is
The image shown has two triangles sharing a vertex:
What is the measure of ∠TVU, and why?
a) y, because Triangle RST is similar to triangle VUT
b) y over 2, because Triangle RST is congruent to triangle VUT
c) y + 55 degrees, because Triangle RST is similar to triangle TUV
1d) 25 degrees − y, because Triangle RST is congruent to triangle TUV
The picture of the question in the attached figure
we know that
If two triangles are similar, then the ratio of its sides is proportional and its corresponding angles are congruent
In this problem
Triangle RST and Triangle VUT are similar ----> by AA Similarity Theorem
because
[tex]m\angle RST=m\angle VUT=55^o[/tex] ---> given value
[tex]m\angle RTS=m\angle VTU[/tex] ----> by vertical angles
so
[tex]m\angle TVU=m\angle TRS[/tex] ----> by corresponding angles in similar triangles
therefore
[tex]m\angle TVU=y^o[/tex]
