Question

In triangle TUV show to the side,What is the measure of angle of TVU in degrees

Answer 1

y, because Triangle RST is similar to triangle VUT

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

`m\angle RST=m\angle VUT=55^o` ---> given value

`m\angle RTS=m\angle VTU` ----> by vertical angles

so

`m\angle TVU=m\angle TRS` ----> by corresponding angles in similar triangles

therefore

`m\angle TVU=y^o`