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$d\parallel {d}'\Rightarrow x+y=180{}^\circ $ $c\parallel {c}'\Rightarrow {{\hat{O}}_{1}}=\frac{y}{2}$ $c\parallel {c}'\Rightarrow {{\hat{M}}_{1}}=\frac{x}{2}$ $OMN:{{\hat{M}}_{1}}+{{\hat{O}}_{1}}+\hat{Z}=180{}^\circ \Rightarrow \frac{x}{2}+\frac{y}{2}+\hat{z}=180{}^\circ \Rightarrow 90+\hat{z}=180{}^\circ \Rightarrow \hat{z}=90$