Question

find the value of x.
7)
(2x + 14)°
(3x + 1)°

Explanation:

Step1: Identify the angle relationship

The two angles \((2x + 14)^\circ\) and \((3x + 1)^\circ\) are vertical angles? Wait, no, looking at the diagram, actually, if we assume that the two angles are equal (maybe vertical angles or something else, but from the diagram, it seems like they are equal? Wait, no, maybe supplementary? Wait, no, let's check again. Wait, maybe the two angles are equal? Wait, no, perhaps the diagram shows that the two angles are equal? Wait, maybe I made a mistake. Wait, actually, looking at the diagram, the two angles \((2x + 14)^\circ\) and \((3x + 1)^\circ\) are equal? Wait, no, maybe they are vertical angles? Wait, no, vertical angles are equal. Wait, maybe the diagram is such that the two angles are equal. So we set them equal:

\(2x + 14 = 3x + 1\)

Step2: Solve for x

Subtract \(2x\) from both sides:

\(14 = x + 1\)

Subtract 1 from both sides:

\(x = 13\)

Wait, but maybe I misinterpreted the diagram. Wait, maybe the two angles are supplementary? Wait, no, the diagram shows two angles with a common vertex, and maybe they are equal. Wait, let's re-examine. If the two angles are vertical angles, then they are equal. So the equation is \(2x + 14 = 3x + 1\). Solving:

\(2x + 14 = 3x + 1\)

Subtract \(2x\) from both sides: \(14 = x + 1\)

Subtract 1: \(x = 13\)

Answer:

\(x = 13\)