Since XY = YZ, we know that ΔXYZ is isosceles and we have
proved that the base angles of an isosceles triangle are
equal.  So ∠X = ∠Z

We have also proved that the sum of the three interior angles of 
any triangle is 180°.

Therefore ∠X + ∠Y + ∠Z = 180°, and since ∠X = ∠Z,
we can substitute ∠X for ∠Z, and also 42° for ∠Y and get:

          ∠X + 42° + ∠X = 180°

              2∠X + 42° = 180°

Subtract 42° from both sides gives:

                    2∠X = 138°

Dividing both sides by 2

                     ∠X = 69°

Edwin