Question

ASAP!!!!

Answer 1

Answer:

The value of x is 45

Step-by-step explanation:

Statement 1: Segment ST is parallel to segment RQ.      

Reason: Given

Statement 2: Angle QRS is congruent to angle TSP.

Reason : Corresponding angles formed by parallel lines and their transversal are congruent.

Statement 3: Angle SPT is congruent to angle RPQ.

Reason:  Reflexive property of angles

Statement 4: Triangle SPT is similar to triangle RPQ.

Reason: Angle-Angle Similarity Postulate

So, ΔSPT≈ΔRPQ

5. Corresponding sides of similar triangles are in proportion.

$\frac{SP}{PR}=\frac{PT}{PQ}\\\frac{60}{60+x}=\frac{48}{48+36}\\60(48+36)=48(60+x)\\5040=2880+48x\\5040-2880=48x\\2160=48x\\\frac{2160}{48}=x\\45=x$

Hence The value of x is 45