Question

△rst and △utv are shown below.
which statement is true?
△rst is similar to △utv.
△rst is not similar to △utv.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find ∠RTS in △RST

In right △RST, sum of angles is 180°.
$\angle RTS = 180^\circ - 90^\circ - 39^\circ = 51^\circ$

Step2: Find ∠U in △UTV

In right △UTV, sum of angles is 180°.
$\angle U = 180^\circ - 90^\circ - 61^\circ = 29^\circ$

Step3: Compare triangle angle sets

△RST angles: $90^\circ, 39^\circ, 51^\circ$
△UTV angles: $90^\circ, 61^\circ, 29^\circ$
No matching non-right angle pairs.

Answer:

△RST is not similar to △UTV.