Answer:
x = 5
Step-by-step explanation:
Since ∠P ≅ ∠P and ∠PST≅ ∠PRQ (corresponding angles are congruent when the lines are parallel), ΔPST is similar to ΔPRQ by the AA postulate
Therefore, corresponding sides are in proportion.
PS ↔ PR and ST ↔ RQ
[tex]\frac{PS}{PR} = \frac{ST}{RQ} \\\frac{x + 7}{2x + 6} = \frac{6}{8}[/tex] Note: PR = PS + SR = x + 7 + x - 1 = 2x + 6
8(x + 7) = 6(2x + 6)
8x+56 = 12x + 36
4x = 20
x = 5
