\[\boxed{\mathbf{1345.еуроки - ответы\ на\ пятёрку}}\]
\[\textbf{а)}\ k = \frac{8}{18} = \frac{4}{9}.\]
\[z = 12 \cdot \frac{4}{9} = \frac{16}{3} = 5\frac{1}{3};\]
\[x = 15 \cdot \frac{4}{9} = \frac{20}{3} = 6\frac{2}{3};\]
\[y = 21 \cdot \frac{4}{9} = \frac{28}{3} = 9\frac{1}{3}.\]
\[\alpha = 60{^\circ};\]
\[\beta = 110{^\circ}.\]
\[\textbf{б)}\ k = \frac{12}{18} = \frac{2}{3}.\]
\[x = 21 \cdot \frac{2}{3} = 14;\]
\[z = 27 \cdot \frac{2}{3} = 18;\]
\[y = 18 \cdot \frac{3}{2} = 27.\]
\[\alpha = 50{^\circ};\]
\[\beta = 70{^\circ}.\]