Answer:
[tex]\boxed{\boxed{w^{\circ}+x^{\circ}+y^{\circ}+z^{\circ}=180^{\circ}}}[/tex]
Step-by-step explanation:
Given that PQST is a parallelogram, so
[tex]\Rightarrow QS\ ||\ PT[/tex]
As a parallelogram is a quadrilateral with both pairs of opposite sides parallel.
PR and RT are the transversal to the parallel lines QS and PT, so
[tex]\Rightarrow m\angle QRP=m\angle RPT\ and\ m\angle SRT=m\angle RTP[/tex]
As they are alternate interior angles.
Hence,
[tex]\Rightarrow m\angle RPT=x^{\circ}\ and\ m\angle RTP=y^{\circ}[/tex]
When the two lines being crossed are parallel lines the consecutive interior angles add up to 180°.
So, [tex]m\angle QPT+m\angle STP=180^{\circ}[/tex]
[tex]\Rightarrow m\angle QPR+m\angle RPT+m\angle RTP+m\angle RTS=180^{\circ}[/tex]
[tex]\Rightarrow w^{\circ}+x^{\circ}+y^{\circ}+z^{\circ}=180^{\circ}[/tex]
