Question

the diagram below shows three intersecting lines.
what is the measure of \\(\angle x\\)?

Explanation:

Step1: Recall straight angle property

A straight angle measures \(180^\circ\). The angles on a straight line sum to \(180^\circ\).

Step2: Identify known angles

We have angles \(53^\circ\), \(51^\circ\), and \(x\) on a straight line. Wait, actually, using vertical angles and linear pair. Wait, the three lines intersect, so the sum of angles around a point? No, for the straight line (horizontal line), the angles adjacent to \(x\): the vertical angle of \(53^\circ\) is equal, and the angle \(51^\circ\), so \(x + 51^\circ+ 53^\circ= 180^\circ - 90^\circ\)? Wait, no, let's correct. The horizontal line is a straight line, so the sum of angles on one side of the horizontal line is \(180^\circ\). Wait, the angle \(53^\circ\), the angle \(51^\circ\), and \(x\) should sum to \(180^\circ - 90^\circ\)? No, better: the sum of angles on a straight line (180 degrees). So \(x + 51^\circ+ 53^\circ= 180^\circ - 0^\circ\)? Wait, no, let's see: the three angles (53°, 51°, and x) are on a straight line, so their sum is 180°. Wait, no, actually, the vertical angle of 53° is equal, and the angle 51°, so x + 51° + 53° = 180°? Wait, no, 180 - 53 - 51 = 76? Wait, 53 + 51 = 104, 180 - 104 = 76. Wait, let's check:

Wait, the horizontal line is a straight angle (180°). The angles formed with the other lines: one angle is 53°, another is 51°, and x. So 53 + 51 + x = 180? Wait, no, maybe the right angle? Wait, no, the diagram: three intersecting lines, so the horizontal line, and two other lines. The angle between the two non-horizontal lines: 51°, and the angle with the horizontal and one line is 53°, so x is the remaining angle. So 180 - 53 - 51 = 76. So x = 180 - 53 - 51 = 76.

Wait, step by step:

1. The sum of angles on a straight line is \(180^\circ\).
2. We have three angles: \(53^\circ\), \(51^\circ\), and \(x\) on the straight line.
3. So \(x = 180^\circ - 53^\circ - 51^\circ\).
4. Calculate: \(180 - 53 - 51 = 76\).

Answer:

\(76\)