Answer:
m∠WZX = 41°
m∠WZY = 107°
Explanation:
Note: There is an error in the question. The correct angle is WXZ = 31°.
If WXYZ is a quadrilateral, then XZ is one of its diagonals.
This means that WXZ is a triangle with vertices:
- ∠WXZ = 31°
- ∠ZWX = 108°
- ∠WZX
Interior angles of a triangle sum to 180°. Therefore:
⇒ m∠WXZ + m∠ZWX + m∠WZX = 180°
⇒ 31° + 108° + m∠WZX = 180°
⇒ 139° + m∠WZX = 180°
⇒ m∠WZX = 41°
Interior angles of a quadrilateral sum to 360°. Therefore:
⇒ m∠W + m∠X + m∠Y + m∠Z = 360°
⇒ 108° + 88° + 57° + m∠Z = 360°
⇒ 253° + m∠Z = 360°
⇒ 253° + m∠Z = 360°
⇒ m∠Z = 107°
As angle WZY is the same as angle Z, m∠WZY = 107°.