Question

1. calculate the value of x in the following diagram.

4x°
120°

Explanation:

Step1: Identify angle relationship

The angles \(4x^\circ\) and \(120^\circ\) are vertical angles? No, wait, actually, when two lines intersect, vertical angles are equal, but also, adjacent angles are supplementary? Wait, no, looking at the diagram, the two angles \(4x\) and \(120^\circ\) – wait, maybe they are vertical angles? Wait, no, maybe they are supplementary? Wait, no, let's check: when two lines intersect, the sum of adjacent angles is \(180^\circ\), but vertical angles are equal. Wait, in the diagram, the angle \(4x\) and \(120^\circ\) – wait, maybe they are equal? Wait, no, maybe I made a mistake. Wait, no, actually, if the two angles are vertical angles, then \(4x = 120\)? Wait, no, that would give \(x = 30\), but let's check. Wait, no, maybe the angle \(4x\) and \(120^\circ\) are supplementary? Wait, no, let's think again. Wait, the diagram shows two intersecting lines, so the angle \(4x\) and the \(120^\circ\) angle – are they adjacent? Wait, maybe the angle \(4x\) and \(120^\circ\) are vertical angles? Wait, no, vertical angles are opposite each other. Wait, maybe the angle \(4x\) and \(120^\circ\) are equal? Wait, no, that can't be. Wait, maybe I misread. Wait, the problem: the diagram has two intersecting lines, with one angle \(120^\circ\) and another angle \(4x\). Wait, actually, when two lines intersect, the vertical angles are equal, and the adjacent angles are supplementary. Wait, maybe the angle \(4x\) and \(120^\circ\) are supplementary? No, wait, no – wait, maybe the angle \(4x\) and \(120^\circ\) are equal? Wait, no, that would mean \(4x = 120\), so \(x = 30\). Wait, but let's check: if \(x = 30\), then \(4x = 120\), so the two angles are equal, which are vertical angles. Yes, vertical angles are equal. So the equation is \(4x = 120\).

Step2: Solve for x

Divide both sides by 4: \(x=\frac{120}{4}\)
\(x = 30\)

Answer:

\(x = 30\)