Question

fencing x-braces are also used to provide support in rectangular fencing. if $ab = 6$ feet, $ad = 2$ feet, and $m\angle dae = 65^\circ$, find $m\angle ceb$. round to the nearest tenth, if necessary
$m\angle ceb =$

Explanation:

Step1: Identify rectangle properties

Since \(ABCD\) is a rectangle, \(AB = DC = 6\) ft, \(AD = BC = 2\) ft, and \(\angle ADE = \angle BCE = 90^\circ\). Also, \(\triangle ADE \cong \triangle BCE\) (HL congruence), so \(\angle BCE = \angle ADE = 90^\circ\), and \(\angle DAE = \angle BCE = 65^\circ\).

Step2: Find \(\angle AED\)

In \(\triangle ADE\), sum of angles is \(180^\circ\).
\(\angle AED = 180^\circ - 90^\circ - 65^\circ = 25^\circ\)

Step3: Relate \(\angle AED\) to \(\angle CEB\)

\(\angle AED\) and \(\angle CEB\) are vertical angles, so they are equal.
\(m\angle CEB = m\angle AED = 25^\circ\)

Answer:

\(25.0^\circ\)