Question

1. find x

a) 28 b) 5 c) 55 d) 40

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. The angle \((3x - 35)^\circ\) and \(130^\circ\) are vertical angles? Wait, no, actually, adjacent angles on a straight line are supplementary, but here \((3x - 35)^\circ\) and \(130^\circ\) are equal? Wait, no, looking at the diagram, lines AB and CD intersect at O. So \((3x - 35)^\circ\) and \(130^\circ\) are equal? Wait, no, maybe they are vertical angles? Wait, no, let's check: when two lines intersect, vertical angles are equal. Wait, maybe \((3x - 35)^\circ\) is equal to \(130^\circ\)? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, no, actually, adjacent angles on a straight line sum to \(180^\circ\), but here, if we look at the angles around point O, the angle \((3x - 35)^\circ\) and \(130^\circ\) are vertical angles? Wait, no, let's re-examine. Wait, the angle labeled \((3x - 35)^\circ\) and the \(130^\circ\) angle: are they vertical angles? Yes, because when two lines intersect, vertical angles are equal. So we set \(3x - 35 = 130\)? Wait, no, that would give \(3x = 165\), \(x = 55\), but let's check the options. Option c is 55. Wait, but let's confirm. Wait, maybe I messed up. Wait, no, vertical angles are equal. So if \((3x - 35)^\circ\) and \(130^\circ\) are vertical angles, then \(3x - 35 = 130\). Solving for x:

Step2: Solve for x

\(3x - 35 = 130\)

Add 35 to both sides: \(3x = 130 + 35 = 165\)

Divide both sides by 3: \(x = \frac{165}{3} = 55\)

Answer:

c) 55