Question

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

Explanation:

Step1: Find ∠TVU

∠TVU = 66° (vertical angles are equal)

Step2: Calculate ∠T in △TUV

Sum of angles in triangle is 180°.
$\angle T = 180^\circ - 24^\circ - 66^\circ = 90^\circ$

Step3: Identify angles in △WXV

∠W = 90°, ∠WVX = 66°, so $\angle X = 180^\circ - 90^\circ - 66^\circ = 24^\circ$

Step4: Match corresponding angles

△TUV: ∠T=90°, ∠U=24°, ∠TVU=66°
△WXV: ∠W=90°, ∠X=24°, ∠WVX=66°
All corresponding angles are equal.

Answer:

△TUV is similar to △WXV.