Question

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

Explanation:

Step1: Find ∠T in △PRT

Sum of angles in triangle is $180^\circ$.
$\angle T = 180^\circ - 86^\circ - 39^\circ = 55^\circ$

Step2: Find ∠SRQ in △SRQ

$\angle SRQ = 86^\circ$ (shared angle with △PRT)
Find ∠RSQ:
$\angle RSQ = 180^\circ - 86^\circ - 51^\circ = 43^\circ$

Step3: Compare triangle angle sets

△PRT angles: $86^\circ, 39^\circ, 55^\circ$
△SRQ angles: $86^\circ, 51^\circ, 43^\circ$
No matching pair of equal corresponding angles beyond the shared angle.

Answer:

$\triangle PRT$ is not similar to $\triangle SRQ$.