Question

the two lines shown in the figure are parallel.
what is the value of x?

Explanation:

Step1: Find adjacent angle to 134°

The angle adjacent to \(134^\circ\) on the straight line is \(180 - 134 = 46^\circ\) (linear pair).

Step2: Sum of angles in triangle

In a triangle, sum of angles is \(180^\circ\). We have angles \(46^\circ\), \(2x^\circ\), and \(56^\circ\). So \(46 + 2x + 56 = 180\).

Step3: Solve for x

Simplify: \(102 + 2x = 180\). Subtract 102: \(2x = 78\). Divide by 2: \(x = 39\).

Answer:

\(39\)