Respuesta :

[tex]\bf \stackrel{\measuredangle A}{(5x-14)}+\stackrel{\measuredangle D}{(4x+5)}=\stackrel{\textit{linear angles}}{180}\implies 9x-9=180 \\\\\\ 9x=171\implies x=\cfrac{171}{9}\implies x=19 \\\\[-0.35em] ~\dotfill\\\\ \overline{DC}\implies -2x+54\implies -2(19)+54\implies -38+54\implies 16[/tex]

Answer:

DC = 12

Step-by-step explanation:

In a parallelogram consecutive angles are supplementary, that is

∠DAB and ∠ADC are consecutive and supplementary, thus

5x - 14 + 4x + 5 = 180

9x - 9 = 180 ( add 9 to both sides )

9x = 189 ( divide both sides by 9 )

x = 21

Hence

DC = - 2x + 54 = (- 2 × 21) + 54 = - 42 + 54 = 12

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