Question

Find the value of x will mark brainliest

Answer 1

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

$\frac{PS}{PR} = \frac{ST}{RQ} \\\frac{x + 7}{2x + 6} = \frac{6}{8}$   Note:  PR = PS + SR = x + 7 + x - 1 = 2x + 6

8(x + 7) = 6(2x + 6)

8x+56 = 12x + 36

4x = 20

x = 5