Question

If AACB = ADCE, ZCAB = 63°,ZECD = 52°, and ZDEC = 5xDE(c сx = [?]

Answer 1

Since angles ACB and ECD are vertical angles, they are congruent, so we have

Calculating the sum of internal angles in triangle ABC, we have:

`\begin{gathered} ABC+ACB+CAB=180 \\ ABC+52+63=180 \\ ABC=180-52-63 \\ ABC=65 \end{gathered}`

Since triangles ACB and DCE are congruent, we have
`\begin{gathered} DEC=ABC \\ 5x=65 \\ x=13 \end{gathered}`