Question

in the figure below, \\( \triangle b c d \\) is drawn. the line \\( \overleftrightarrow { e b f } \\) is drawn such that \\( \overleftrightarrow { e b f } \parallel \overleftrightarrow { c d } \\).

Explanation:

Step1: Recall the property of angles on a straight line

The sum of angles on a straight line is \(180^{\circ}\). In this case, the three angles \(53^{\circ}\), \(x^{\circ}\), and \(39^{\circ}\) form a straight line.

Step2: Set up the equation

We can set up the equation \(53 + x+ 39=180\).

Step3: Solve for \(x\)

First, simplify the left - hand side of the equation: \(53 + 39+x=92 + x\). Then, solve for \(x\) using the equation \(92+x = 180\). Subtract 92 from both sides: \(x=180 - 92\). So, \(x = 49\).

Answer:

\(x = 49\)