A few properties of a parallelogram.
1) Opposite sides are always equal.
2) Opposite angles are always equal.
3) The sum of all the angles is 360.
In part 2, we are given the angles. Therefore, we can apply the 2nd property.
11x = 55
5y = z (lets say the unknown is z).
Now, 11x = 55
x = 55/11
x = 5
Now, we have to angles of 55 degrees but we don't know about y and z. Therefore, we have to apply the third property.
55 + 55 + 5y + z = 360
110 + 5y + z = 360
5y + z = 360 -110
5y + z = 250. (i)
According to property 2, 5y = z. Hence, put the value of 5y in the equation (i), we get
5y + z = 250
z + z = 250
2z = 250
z = 250/2
z = 125
From the value of z, we can find the value of y using z = 5y
125 = 5y
5y = 125
y = 125/5
y = 25
Hence, x = 5 and y = 25