Question

1. 2x° 56°

Explanation:

Step1: Identify vertical angles

Vertical angles are equal, so \(2x = 56\) is incorrect. Wait, no—wait, actually, the angles \(2x^\circ\) and \(56^\circ\) are vertical angles? Wait, no, looking at the diagram, the two angles \(2x^\circ\) and \(56^\circ\) are vertical angles? Wait, no, maybe I missee. Wait, vertical angles are opposite each other when two lines intersect. So if two lines intersect, the opposite angles are equal. So if one angle is \(2x\) and the other is \(56^\circ\), are they vertical angles? Wait, maybe the diagram shows that \(2x\) and \(56^\circ\) are vertical angles? Wait, no, maybe I made a mistake. Wait, no—wait, actually, when two lines intersect, vertical angles are equal. So if \(2x\) and \(56^\circ\) are vertical angles, then \(2x = 56\)? No, that can't be. Wait, maybe the angles are supplementary? Wait, no, let's re-examine. Wait, the diagram: two lines intersect, forming vertical angles. So the angle \(2x^\circ\) and the angle \(56^\circ\) are vertical angles? Wait, no, maybe the angle \(2x\) and \(56^\circ\) are vertical angles, so they should be equal? Wait, no, that would mean \(2x = 56\), so \(x = 28\). Wait, but maybe I got the diagram wrong. Wait, the user's diagram: two triangles, with their sides intersecting, forming vertical angles. So the angle labeled \(2x^\circ\) and the angle labeled \(56^\circ\) are vertical angles, so they are equal. So \(2x = 56\)? Wait, no, that would be if they are vertical angles. Wait, vertical angles are equal, so \(2x = 56\)? Wait, no, maybe the angles are supplementary? Wait, no, vertical angles are equal. So let's proceed.

Step1: Recognize vertical angles

The angles \(2x^\circ\) and \(56^\circ\) are vertical angles, so they are equal. Thus, \(2x = 56\).

Step2: Solve for \(x\)

Divide both sides by 2: \(x = \frac{56}{2} = 28\).

Answer:

\(x = 28\)