a triangle,side ac is 3/5 of side ab,and is 23.1 m. side ab is 7/9 of side bc.angle b is 1.5 times larger than angle c,and angle a is twice the size of angle c.how many degrees is angle A

ignore all that noise about side lengths. Working with the angles,

b = 3/2 c
a = 2c

a+b+c = 180
2c + 3/2 c + c = 180
9c = 360
c = 40
so,
a = 80
b = 60

you can check on the side lengths of you wish, to make sure they obey the law of sines.