Question

in the following figure, \\( \overline { e b } \\) and \\( \overline { d c } \\) intersect at point a. what is the value of \\( x \\) in the figure? \\( x = \\)

Explanation:

Step1: Determine the congruent triangles

Since \(AE = AC = 3.9\), \(AD=AB = 3.1\), and \(\angle EAD=\angle CAB\) (vertical angles are equal), by the Side - Angle - Side (SAS) congruence criterion, \(\triangle EAD\cong\triangle CAB\).

Step2: Use the property of congruent triangles

In congruent triangles, corresponding angles are equal. So, \(\angle E=\angle C\).
In \(\triangle ABC\), we know that the sum of angles in a triangle is \(180^{\circ}\). Let's first find the measure of \(\angle BAC\). \(\angle BAC=180^{\circ}-(36^{\circ} + 49^{\circ})=95^{\circ}\). But since \(\triangle EAD\cong\triangle CAB\), and we use the angle - angle relationship.
Another way: Since \(\triangle EAD\cong\triangle CAB\), then \(x = 49^{\circ}\) (corresponding angles of congruent triangles).

Answer:

\(49\)