The angles 182 - 4x and 5x +2 are vertically opposite angles, therefore, they are equal, thus
182-4x = 5x +2
180 =9x, x =180/9 =20 degrees
the angles 182-4x and 4y+2 are corresponding angles, meaning also that they are equal, thus
182 - 4x = 4y +2
but we got x= 20, lets substitute it in
182 - 4(20)= 4y +2
182-80 =4y +2
102 = 4y +2
102-2 =4y
100 =4y, y =100/4 =25 degrees
therefore, x =20 degrees and y = 25 degrees.