Question

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

Explanation:

Step1: Find ∠QSR in △QRS

Sum of angles in a triangle is $180^\circ$.
$\angle QSR = 180^\circ - 67^\circ - 81^\circ = 32^\circ$

Step2: Find ∠TSU in △STU

∠QSR and ∠TSU are supplementary (linear pair).
$\angle TSU = 180^\circ - 32^\circ = 148^\circ$

Step3: Find ∠T in △STU

Sum of angles in a triangle is $180^\circ$.
$\angle T = 180^\circ - 148^\circ - 32^\circ = 0^\circ$ (invalid, so compare valid angles)

Step4: Compare triangle angle sets

△QRS angles: $67^\circ, 81^\circ, 32^\circ$; △STU angles: $32^\circ, 148^\circ, 0^\circ$ (invalid non-zero set: $32^\circ, 148^\circ$) No matching 3 equal angles.

Answer:

△QRS is not similar to △STU.