Question

3 (30x + 4)° 86°

Explanation:

Step1: Identify angle relationship

The two angles \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles? Wait, no, actually, looking at the diagram, they are adjacent and form a linear pair? Wait, no, the two angles \((30x + 4)^\circ\) and \(56^\circ\) are actually equal? Wait, no, wait, the vertical angles? Wait, no, the two angles shown: one is \((30x + 4)^\circ\) and the other is \(56^\circ\), and they are vertical angles? Wait, no, actually, if the lines are intersecting, then vertical angles are equal. Wait, no, maybe they are supplementary? Wait, no, let's check again. Wait, the diagram has two intersecting lines, one vertical and one horizontal? Wait, no, the two angles: \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles? Wait, no, vertical angles are equal. Wait, maybe I made a mistake. Wait, no, actually, the two angles \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles, so they should be equal. Wait, no, wait, maybe they are supplementary? Wait, no, let's see: if the lines are intersecting, then adjacent angles are supplementary, but vertical angles are equal. Wait, the angle \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles? Wait, no, maybe the angle \((30x + 4)^\circ\) and \(56^\circ\) are equal because they are vertical angles. Wait, let's set up the equation: \(30x + 4 = 56\)? Wait, no, that would be if they are vertical angles. Wait, but maybe they are supplementary? Wait, no, if the lines are perpendicular? No, the diagram shows two intersecting lines, one with an angle of \(56^\circ\) and the other with \((30x + 4)^\circ\). Wait, maybe the two angles are vertical angles, so they are equal. So:

\(30x + 4 = 56\)

Step2: Solve for x

Subtract 4 from both sides:

\(30x = 56 - 4\)

\(30x = 52\)? Wait, no, 56 - 4 is 52? Wait, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? Wait, 56 - 4 = 52? Wait, no, 56 - 4 is 52? Wait, 56 - 4 = 52? 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Answer:

Step1: Identify angle relationship

The two angles \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles? Wait, no, actually, looking at the diagram, they are adjacent and form a linear pair? Wait, no, the two angles \((30x + 4)^\circ\) and \(56^\circ\) are actually equal? Wait, no, wait, the vertical angles? Wait, no, the two angles shown: one is \((30x + 4)^\circ\) and the other is \(56^\circ\), and they are vertical angles? Wait, no, actually, if the lines are intersecting, then vertical angles are equal. Wait, no, maybe they are supplementary? Wait, no, let's check again. Wait, the diagram has two intersecting lines, one vertical and one horizontal? Wait, no, the two angles: \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles? Wait, no, vertical angles are equal. Wait, maybe I made a mistake. Wait, no, actually, the two angles \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles, so they should be equal. Wait, no, wait, maybe they are supplementary? Wait, no, let's see: if the lines are intersecting, then adjacent angles are supplementary, but vertical angles are equal. Wait, the angle \((30x + 4)^\circ\) and \(56^\circ\) are vertical angles? Wait, no, maybe the angle \((30x + 4)^\circ\) and \(56^\circ\) are equal because they are vertical angles. Wait, let's set up the equation: \(30x + 4 = 56\)? Wait, no, that would be if they are vertical angles. Wait, but maybe they are supplementary? Wait, no, if the lines are perpendicular? No, the diagram shows two intersecting lines, one with an angle of \(56^\circ\) and the other with \((30x + 4)^\circ\). Wait, maybe the two angles are vertical angles, so they are equal. So:

\(30x + 4 = 56\)

Step2: Solve for x

Subtract 4 from both sides:

\(30x = 56 - 4\)

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