![x = 7](/tpl/images/1016/3944/fa1fc.png)
![y=12](/tpl/images/1016/3944/bddb7.png)
![PQ = 29](/tpl/images/1016/3944/87638.png)
![QR = 29](/tpl/images/1016/3944/9484b.png)
![PS = 32](/tpl/images/1016/3944/443cc.png)
![PT = 18](/tpl/images/1016/3944/854d3.png)
![PR = 36](/tpl/images/1016/3944/5e822.png)
Step-by-step explanation:
See attachment for complete question.
From the attachment:
![PQ = 5y - 31](/tpl/images/1016/3944/205b6.png)
![QR = 2y + 5](/tpl/images/1016/3944/d99a6.png)
![PT = 6x - 2y](/tpl/images/1016/3944/688c9.png)
![PS = 4x +4](/tpl/images/1016/3944/d58d3.png)
![SR = 7x - 17](/tpl/images/1016/3944/3a86a.png)
Solving (a) The value of x
From the attachment:
![PS = SR](/tpl/images/1016/3944/70694.png)
So:
![4x + 4 = 7x - 17](/tpl/images/1016/3944/6d67c.png)
Collect Like Terms
![17+ 4 = 7x -4x](/tpl/images/1016/3944/5bec8.png)
![21 = 3x](/tpl/images/1016/3944/13ded.png)
Make x the subject
![x = \frac{21}{3}](/tpl/images/1016/3944/a6383.png)
![x = 7](/tpl/images/1016/3944/fa1fc.png)
Solving (b): The value of y
![PQ = QR](/tpl/images/1016/3944/61b09.png)
So, we have:
![5y - 31 = 2y + 5](/tpl/images/1016/3944/991f7.png)
Collect Like Terms
![5y - 2y = 5+31](/tpl/images/1016/3944/6f77a.png)
![3y = 36](/tpl/images/1016/3944/06074.png)
Make y the subject
![y = \frac{36}{3}](/tpl/images/1016/3944/1ec81.png)
![y=12](/tpl/images/1016/3944/bddb7.png)
Solving (c): The value of PQ
![PQ = 5y - 31](/tpl/images/1016/3944/205b6.png)
Substitute 12 for y
![PQ = 5*12-31](/tpl/images/1016/3944/25f61.png)
![PQ = 29](/tpl/images/1016/3944/87638.png)
Solving (d): The value of QR
![PQ = QR = 29](/tpl/images/1016/3944/60811.png)
Solving (e): The value of PS
![PS = 4x +4](/tpl/images/1016/3944/d58d3.png)
Substitute 7 for x
![PS = 4 * 7 + 4](/tpl/images/1016/3944/32d13.png)
![PS = 32](/tpl/images/1016/3944/443cc.png)
Solving (f): The value of PT
![PT = 6x - 2y](/tpl/images/1016/3944/688c9.png)
Substitute 7 for x and 12 for y
![PT = 6 * 7 - 2 * 12](/tpl/images/1016/3944/0f223.png)
![PT = 18](/tpl/images/1016/3944/854d3.png)
Solving (g): The value of PR
![PR = PT + TR](/tpl/images/1016/3944/89beb.png)
Because QT bisects PR,
![PT = TR](/tpl/images/1016/3944/578de.png)
So:
![PR = PT + PT](/tpl/images/1016/3944/a88fe.png)
![PR = 18+18](/tpl/images/1016/3944/4961a.png)
![PR = 36](/tpl/images/1016/3944/5e822.png)
![If QT is the perpendicular bisector of PR, find each measure.
5y-31
y =
Р
6x - 2y
2y + 5
PQ =
QR =](/tpl/images/1016/3944/91294.jpg)