Find the 10

Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?

Correct result:

t1 =  2
A1 =  -38.6598 °
A2 =  -128.6598 °
t2 =  -3.125
B1 =  51.3402 °
B2 =  -128.6598 °

Solution:

2tx+5y6=0 5x4y+8=0  n1=(2t;5) n2=(5;4)   normal n1.n2=0   2 t1 5+5 (4)=0  10t1=20  t1=2
A1=180πarctan52 t190=180πarctan52 290=38.6598=383935"
A2=180πarctan4590=128.6598=1283935"
parallel n1=k n2 k=5/(4)=54=1.25   2 t2=5/(4) 5  2t2=6.25  t2=258=3.125=258
B1=180πarctan52 t290=180πarctan52 (3.125)90=51.3402=512025"
B2=180πarctan4590=128.6598=1283935"



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