Question

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

Explanation:

Step1: Find ∠R in △RST

Sum of angles in a triangle is $180^\circ$.
$\angle R = 180^\circ - 112^\circ - 19^\circ = 49^\circ$

Step2: Find ∠V in △UVW

Sum of angles in a triangle is $180^\circ$.
$\angle V = 180^\circ - 49^\circ - 19^\circ = 112^\circ$

Step3: Compare triangle angles

In △RST: $\angle R=49^\circ$, $\angle S=112^\circ$, $\angle T=19^\circ$
In △UVW: $\angle U=49^\circ$, $\angle V=112^\circ$, $\angle W=19^\circ$
All corresponding angles are equal, so triangles are similar by AA similarity.

Answer:

$\triangle RST$ is similar to $\triangle UVW$.