Question

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

Explanation:

Step1: Calculate ∠Q in △QSU

First, find the missing angle in △QSU. The sum of angles in a triangle is $180^\circ$. We know ∠U = $40^\circ$, and ∠S (shared angle) = $88^\circ$.
$\angle Q = 180^\circ - 40^\circ - 88^\circ = 52^\circ$

Step2: Calculate ∠T in △RST

Find the missing angle in △RST. Sum of angles is $180^\circ$, ∠R = $50^\circ$, ∠S = $88^\circ$.
$\angle T = 180^\circ - 50^\circ - 88^\circ = 42^\circ$

Step3: Compare triangle angle sets

△QSU angles: $52^\circ, 88^\circ, 40^\circ$
△RST angles: $50^\circ, 88^\circ, 42^\circ$
No matching pairs of equal corresponding angles.

Answer:

△QSU is not similar to △RST.