Question

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

Answer 1

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:

`\begin{gathered} CDE+DEC+DCE=180 \\ 74+DEC+48=180 \\ \text{DEC}=180-74-48 \\ DEC=58\degree \end{gathered}`

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