Question

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

Explanation:

Step1: Calculate ∠STR in △RST

Sum of angles in a triangle is $180^\circ$.
$\angle STR = 180^\circ - 72^\circ - 32^\circ = 76^\circ$

Step2: Calculate ∠UTV in △UVT

First find ∠RTS adjacent angle at T: $180^\circ - 76^\circ = 104^\circ$
Then $\angle UTV = 180^\circ - 72^\circ - 104^\circ$? No, correct: use triangle angle sum for △UVT directly.
Wait, correct Step2: Calculate all angles of △UVT
$\angle UTV = 180^\circ - 72^\circ - \angle V$. First confirm △RST angles: $72^\circ, 32^\circ, 76^\circ$. Now, vertical/adjacent angle to ∠STR is $180^\circ -76^\circ=104^\circ$, so $\angle UTV=104^\circ$. Then $\angle V=180^\circ -72^\circ -104^\circ=4^\circ$.

Step3: Compare triangle angle sets

△RST angles: $32^\circ, 72^\circ, 76^\circ$; △UVT angles: $72^\circ, 104^\circ, 4^\circ$. No matching 3 equal angles.

Answer:

△RST is not similar to △UVT.