Question

question
in the diagram below, \\( \overline { a c } \parallel \overline { d g } , \overline { b e } \cong \overline { b f } \\) and \\( m \angle a b h = 65 ^ { \circ } \\). find \\( m \angle d e \\)

answer attempt 1 out of 2

Explanation:

Step1: Find the measure of ∠BFE

Since \( \overline{AC}\parallel\overline{DG}\), \( \angle ABH\) and \( \angle BFE\) are corresponding angles.
By the Corresponding Angles Postulate, \(m\angle BFE = m\angle ABH=65^{\circ}\).

Step2: Use the isosceles triangle property

Given \( \overline{BE}\cong\overline{BF}\), so \(\triangle BEF\) is isosceles. Then \(m\angle BEF=m\angle BFE = 65^{\circ}\).

Step3: Calculate \(m\angle DEB\)

Since \( \angle DEB\) and \( \angle BEF\) form a linear - pair. By the Linear - Pair Postulate, \(m\angle DEB + m\angle BEF=180^{\circ}\).
Substitute \(m\angle BEF = 65^{\circ}\) into the equation: \(m\angle DEB=180^{\circ}-m\angle BEF\).
\(m\angle DEB = 180^{\circ}-65^{\circ}=115^{\circ}\).

Answer:

\(115^{\circ}\)