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Answer:

[tex]AD = 8[/tex], [tex]DC = 15[/tex], [tex]m\,\angle A = 112^{\circ}[/tex], [tex]m\,\angle B = 68^{\circ}[/tex], [tex]m\,\angle C = 112^{\circ}[/tex]

Explanation:

If the quadrilateral presented in figure is a parallelogram, then the following conditions are satisfied:

[tex]AD = BC[/tex] (1)

[tex]AB = DC[/tex] (2)

[tex]m\,\angle D = m\,\angle B[/tex] (3)

[tex]m\,\angle A = m\,\angle C[/tex] (4)

[tex]m\,\angle A + m\,\angle B = 180^{\circ}[/tex] (5)

[tex]m\,\angle C + m\,\angle D = 180^{\circ}[/tex] (6)

If we know that [tex]m\,\angle D = 68^{\circ}[/tex], [tex]AB = 15[/tex] and [tex]BC = 8[/tex], then we have the following results:

[tex]AD = 8[/tex], [tex]DC = 15[/tex], [tex]m\,\angle A = 112^{\circ}[/tex], [tex]m\,\angle B = 68^{\circ}[/tex], [tex]m\,\angle C = 112^{\circ}[/tex]

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