Question

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

Explanation:

Step1: Find ∠S in △RST

First, identify vertical angles: ∠RTS = ∠UTV = 42°. Use triangle angle sum ($180^\circ$) for △RST:
$\angle S = 180^\circ - 66^\circ - 42^\circ = 72^\circ$

Step2: Find ∠V in △VUT

Use triangle angle sum for △VUT:
$\angle V = 180^\circ - 68^\circ - 42^\circ = 70^\circ$

Step3: Compare triangle angle sets

△RST angles: $66^\circ, 42^\circ, 72^\circ$
△VUT angles: $68^\circ, 42^\circ, 70^\circ$
No matching 3-angle sets, so triangles are not similar.

Answer:

△RST is not similar to △VUT.