Question

$\triangle rst$ and $\triangle ruv$ are shown below.
which statement is true?
$\triangle rst$ is similar to $\triangle ruv$.
$\triangle rst$ is not similar to $\triangle ruv$.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate ∠S in △RST

Sum of angles in triangle is $180^\circ$.
$\angle S = 180^\circ - 86^\circ - 41^\circ = 53^\circ$

Step2: Match corresponding angles

In △RST: $\angle R=86^\circ$, $\angle S=53^\circ$, $\angle T=41^\circ$
In △RUV: $\angle R=86^\circ$, $\angle U=53^\circ$, $\angle V=41^\circ$
All corresponding angles are equal.

Step3: Apply similarity rule

Triangles with all corresponding angles equal are similar (AA similarity).

Answer:

$\Delta RST$ is similar to $\Delta RUV$.