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