Question

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

Explanation:

Step1: Find ∠S in △RST

Sum of angles in triangle is $180^\circ$.
$\angle S = 180^\circ - 43^\circ - 55^\circ = 82^\circ$

Step2: Find ∠T in △TUV

Sum of angles in triangle is $180^\circ$.
$\angle T = 180^\circ - 82^\circ - 55^\circ = 43^\circ$

Step3: Match corresponding angles

In △RST: $\angle R=43^\circ$, $\angle S=82^\circ$, $\angle T=55^\circ$
In △TUV: $\angle T=43^\circ$, $\angle U=82^\circ$, $\angle V=55^\circ$
All corresponding angles are equal.

Answer:

△RST is similar to △TUV.