Question

fill in the blank (1 point) (overline{ab} parallel overline{ed}), (ab = ad), (mangle edc = 70^circ), (mangle a =)

Explanation:

Step1: Identify isosceles triangle properties

In $\triangle ABD$, $AB=AD$, so $\angle B = \angle ADB$. Let $\angle B = \angle ADB = x$.

Step2: Use triangle angle sum theorem

The sum of angles in a triangle is $180^\circ$, so:
$$\angle A + \angle B + \angle ADB = 180^\circ$$
$$\angle A + 2x = 180^\circ \quad (1)$$

Step3: Use parallel line properties

Since $\overline{AB} \parallel \overline{ED}$, $\angle B = \angle EDC$ (corresponding angles). Given $m\angle EDC=70^\circ$, so $x=70^\circ$.

Step4: Solve for $\angle A$

Substitute $x=70^\circ$ into equation (1):
$$\angle A + 2\times70^\circ = 180^\circ$$
$$\angle A = 180^\circ - 140^\circ$$

Answer:

$40^\circ$