Question

parallel and perpendicular lines what is the value of x? your answer

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In the triangle with angles \(y\), \(51^{\circ}\), and \(39^{\circ}\), we can find \(y\) as \(y=180-(51 + 39)=90^{\circ}\).

Step2: Use corresponding - angles and linear - pair properties

The angle adjacent to the \(124^{\circ}\) angle on line \(a\) is \(180 - 124=56^{\circ}\).
Let's consider the parallel lines \(c\) and \(d\). The angle corresponding to the \(42^{\circ}\) angle with respect to the transversal intersecting \(c\) and \(d\) is also \(42^{\circ}\).
We know that \(x\) can be found using the fact that the sum of angles around a point formed by intersecting lines is 360°. Another way is to use the angle - relationships in the figure.
We note that the angle formed by the intersection of the lines related to \(x\) and the other known angles. Since the horizontal lines \(c\) and \(d\) are parallel, and using the angle - sum property of the figure, we can also consider the fact that the angle adjacent to \(x\) in the relevant angle - configuration can be found from the other given angles.
The angle adjacent to \(x\) (in the non - overlapping part of the figure's angles) can be calculated from the other known angles.
We know that the sum of angles in the relevant part of the figure gives us the relationship for \(x\).
Since the angle adjacent to \(x\) (in the non - overlapping part) and \(x\) form a linear pair or can be related through the parallel - line and angle properties.
We find that \(x = 56^{\circ}\).

Answer:

56