Find the 10

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

Correct answer:

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

Step-by-step explanation:

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=1020=2  t1=2
A1=π180°arctan2 t1590=π180°arctan2 2590=38.6598=38°3935"
A2=π180°arctan5490=128.6598=128°3935"
parallel n1=k n2 k=5/(4)=45=141=1.25  2 t2=5/(4) 5  2t2=6.25  t2=26.25=3.125  t2=825=3.125
B1=π180°arctan2 t2590=π180°arctan2 (3.125)590=51.3402=51°2025"
B2=π180°arctan5490=128.6598=128°3935"



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