Answer:
Step-by-step explanation:
1) QT = 12
2) m∠PQS = 90 - m∠RQS = 90 - 65 = 25°
3) m∠QRS = 90°
4) ST=15, PR= 2ST = 2(15) = 30
5) QR = 15, then RS = 15
6) m∠QRS = 120, m∠QRP = 60°
7) m∠TPQ + m∠TQP = 90
8) m∠RTS = 90
9) x =?
similar triangles:
AP/(x+5) = RP / (3x-2)
since RP = 2AP
AP(3x-2) = 2(AP)(x+5)
3xAP - 2AP = 2xAP + 10AP
3xAP - 2xAP = 10AP + 2AP
xAP= 12AP
x = 12AP/AP= 12
OR
midpoint is 1/2 the size of the parallel side/base of the bigger triangle.
3x-2 = 2(x+5)
3x -2 = 2x+10
3x-2x = 10+2
x = 12
10) AB = (12+5) = (12+5) = 17
