Question

in the diagram below, ad ≅ ae, ba || ce, cb || da and m∠dae = 50°. find m∠bad. you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale. answer attempt 1 out of 2 m∠bad =

Explanation:

Step1: Identify the isosceles triangle

Since $AD = AE$ and $\angle DAE=50^{\circ}$, in $\triangle ADE$, using the angle - sum property of a triangle ($\angle ADE+\angle AED+\angle DAE = 180^{\circ}$) and the fact that $\angle ADE=\angle AED$ (base - angles of an isosceles triangle are equal), we have $\angle ADE=\angle AED=\frac{180^{\circ}-\angle DAE}{2}=\frac{180 - 50}{2}=65^{\circ}$.

Step2: Use the parallel - line property

Because $CB\parallel DA$ and $BA\parallel CE$, quadrilateral $ABCD$ is a parallelogram. In a parallelogram, opposite angles are equal. Also, $\angle BAD$ and $\angle ADE$ are alternate interior angles. Since $BA\parallel CE$, $\angle BAD=\angle ADE$.

Answer:

$65$