Question

in the diagram below, \\( \overline { a d } \cong \overline { a e } \\), \\( \overline { b a } \parallel \overline { c e } \\), \\( \overline { c b } \parallel \overline { d a } \\) and \\( m \angle b a d = 63 ^ { \circ } \\). find \\( m \angle d a e \\).
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

Explanation:

Step1: 平行四边形性质

因为\(\overline{CB}\parallel\overline{DA}\)，\(\overline{BA}\parallel\overline{CE}\)，所以四边形\(CBAD\)是平行四边形。根据平行四边形性质，\(\angle BAD=\angle CDA = 63^{\circ}\)。

Step2: 等腰三角形性质

因为\(\overline{AD}\cong\overline{AE}\)，所以\(\triangle ADE\)是等腰三角形，\(\angle ADE = 180^{\circ}-\angle CDA=180 - 63=117^{\circ}\)。
根据等腰三角形两底角相等，\(\angle DAE=(180^{\circ}-\angle ADE)\div2=(180 - 117)\div2 = 39^{\circ}\)。

Answer:

\(39^{\circ}\)