From the trapezoid,
x + ( 31 + 38 ) + y = 180 ------------ equ 1
x + y + 69 = 180
x + y = 180 - 69
x + y = 111 .................... equ 2
Also, x + 31 + 90 = 180
x + 121 = 180
x = 180 -121
x = 59.....................equ 3
put x = 59 in equ 2 ,
59 + y = 11
y = 111 - 59
y = 52 ------------------equ 4