Question

in the diagram below, \\(\overline{ad} \cong \overline{ae}\\), \\(\overline{ba} \parallel \overline{ce}\\), \\(\overline{cb} \parallel \overline{da}\\) and \\(m\angle dae = 54^\circ\\). find \\(m\angle bad\\). step angle reason 1 \\(m\angle dae = 54^\circ\\) given try \\(m\angle bad = 117 ^\circ\\) select a reason

Explanation:

Step1: Find base angles of $\triangle AED$

Since $\overline{AD} \cong \overline{AE}$, $\triangle AED$ is isosceles. The sum of angles in a triangle is $180^\circ$, so:
$$\text{m}\angle ADE = \text{m}\angle AED = \frac{180^\circ - 54^\circ}{2} = 63^\circ$$

Step2: Use parallel lines property

$\overline{BA} \parallel \overline{CE}$, so $\angle BAD$ and $\angle ADE$ are same-side interior angles, which are supplementary:
$$\text{m}\angle BAD = 180^\circ - \text{m}\angle ADE = 180^\circ - 63^\circ = 117^\circ$$

Step3: State the final reason

The reason is: Same-side interior angles of parallel lines are supplementary, and base angles of an isosceles triangle are congruent

Answer:

$\text{m}\angle BAD = 117^\circ$