Statements and reasons.
1) WXY is a line and ∠WXZ = 135°
Reasons: This statement is true because it is stated in the question.
2) m∠WXY = 180°
Reasons: This statement is true because the angle of a straight line is always 180°.
3) m∠WXY = m∠WXZ + m∠ZXY
Reasons: This statement is true because the angles on one side of a straight line (m∠WXZ and m∠ZXY) always add to 180°.
4) 180° = 135° + m∠ZXY
Reasons:
- by the definition of the question, we know that ∠WXZ = 135° (statement 1)
- from statement 2 we know that m∠WXY = 180° (statement 2)
- replacing the angles of statement 1 and 2 in the equation of statement 3 we find the equation: 180° = 135° + m∠ZXY
5) 45° = m∠ZXY
Reasons: From statement 4 we find that:
[tex]\begin{gathered} 180^{\circ}=135^{\circ}+m\angle ZXY \\ m\angle ZXY=180^{\circ}-135^{\circ} \\ m\angle ZXY=45^{\circ} \end{gathered}[/tex]In summary, the reasons are:
1) It is stated in the question.
2) The angle of a straight line is always 180°.
3) The angles on one side of a straight line add 180°.
4) Replacing statement 1 and 2 in statement 3.
5) Solving for m∠ZXY the equation of statement 4.
