Answer:
Value of x is 17.5.
Explanation:
Consider the figure given below,
Given : A triangle RST with measure of ∠R= 80° and PQ ║ TS.
RP = 8, PT = 14, RQ= 10 , QS = x
We have to find the value of QS.
Consider ΔRTS AND ΔRPQ,
∠R= 80° =∠R (Common)
PQ ║ TS and RT is transverse, ∠P = ∠T (Alternate angles)
Thus, ΔRTS ≅ ΔRPQ (by AA similarity)
By CPCT,
![(RP)/(RT)=(RQ)/(RS)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/aqt6zyi9gz1ljl96kkci9pujx8e5clmxxa.png)
Substitute values above, we get,
![(8)/(8+14)=(10)/(10+x)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/73d7r9ds3wbdqbd91kijbxat54c8sh39l5.png)
![(8)/(8+14)=(10)/(10+x)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/73d7r9ds3wbdqbd91kijbxat54c8sh39l5.png)
Solve for x, we get,
![(8)/(22)=(10)/(10+x)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/tqq0ybyuydflhjlrmm0thyq6pkz4rq1lrr.png)
![10+x=(220)/(8)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/dt2c3p7io40zv42ogrjsh2x6l17byfcjwf.png)
![10+x=27.5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/72uj91ns2sp9y1u0oc5qc8fay7y1jaxvb7.png)
![x=27.5-10](https://img.qammunity.org/2020/formulas/mathematics/middle-school/wpi7oos0kmjxtfcdbpcv81ed7p9w25zyfd.png)
![x=17.5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ujegqpv4yfjjp69cqn1x3zwba3j8g85ljx.png)
Thus, value of x is 17.5.