Question

determine if triangle pqr and triangle stu are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Find ∠R in △PQR

Sum of angles in a triangle is $180^\circ$.
$\angle R = 180^\circ - 76^\circ - 58^\circ = 46^\circ$

Step2: Find ∠T in △STU

Sum of angles in a triangle is $180^\circ$.
$\angle T = 180^\circ - 45^\circ - 76^\circ = 59^\circ$

Step3: Compare triangle angle sets

△PQR angles: $76^\circ, 58^\circ, 46^\circ$
△STU angles: $76^\circ, 45^\circ, 59^\circ$
No matching set of three equal angles.

Answer:

The triangles are not similar.