It’s non-soluble without a length as the angle changes dependent on the height of the major triangle.
Assume the top triangle is
20
a b
and the complementary angles are c and x, so
20
a b
c x
we need to find a,b,c and x. Four equations and four unknowns;
a+b=160
a+x=150
b+c=140
x+c=130
Now you can solve these either as a matrix and take the inverse of the 4×4 or you can back substitute;
[160] [1100] [a]
[150] = [1001]
[140] [0110] [c]
[130] [0011] [x]
Unfortunately the determinant of this matrix is zero, so there is no inverse. Hence no solution to the four equations. The problem is ill posed.
For back substitution;
c=130-x
b=140-c = 140-(130-x) = 10+x
a+b = a+(10+x) = 160 so a+x = 150
Hence you really only have three equations and four unknowns. That’s why it is on Facebook 😉
Maths is more fun than bike fitting 😉