ElishahH235307 ElishahH235307
  • 26-10-2022
  • Mathematics
contestada

If AABC = ADEC, ZABC = 2x,ZBCA = 489, and LCDE = 740ADEBx = [?]Enter

If AABC ADEC ZABC 2xZBCA 489 and LCDE 740ADEBx Enter class=

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LauranaR465131 LauranaR465131
  • 26-10-2022

Looking at the figure, the angles BCA and DCE are vertical angles, therefore they are congruent.

So, using the sum of internal angles in the triangle DEC, we have:

[tex]\begin{gathered} CDE+DEC+DCE=180 \\ 74+DEC+48=180 \\ \text{DEC}=180-74-48 \\ DEC=58\degree \end{gathered}[/tex]

Since triangles ABC and DEC are congruent, we have [tex]\begin{gathered} ABC=\text{DEC} \\ 2x=58 \\ x=29 \end{gathered}[/tex]

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