Question

cip 2026 math b q3 benchmark
what is the value of x?
(figure with angles 43° and (4x + 7)°)
options: 8.25, 12, 9, 20

Explanation:

Step1: Identify Vertical Angles

The angle of \(43^\circ\) and the angle \((4x + 7)^\circ\) are vertical angles? Wait, no, wait—wait, actually, looking at the diagram, the \(43^\circ\) angle and the angle adjacent to \((4x + 7)^\circ\)? Wait, no, maybe they are complementary? Wait, no, let's check again. Wait, the two angles \(43^\circ\) and \((4x + 7)^\circ\) are actually—wait, no, maybe they are equal? Wait, no, wait, maybe they are supplementary? Wait, no, let's think. Wait, the diagram shows intersecting lines. Wait, the \(43^\circ\) angle and the angle \((4x + 7)^\circ\) are vertical angles? Wait, no, maybe not. Wait, maybe the \(43^\circ\) and \((4x + 7)^\circ\) are such that \(43 + (4x + 7) = 90\)? Wait, no, that would be if they are complementary. Wait, no, maybe they are equal? Wait, no, let's check the options. Wait, let's set up the equation. Wait, maybe the \(43^\circ\) and \((4x + 7)^\circ\) are equal? Wait, no, that would give \(4x + 7 = 43\), so \(4x = 36\), \(x = 9\). Oh, that works. So maybe they are vertical angles? Wait, vertical angles are equal. So if the \(43^\circ\) angle and \((4x + 7)^\circ\) are vertical angles, then they are equal. So:

Step2: Set Up Equation

Set \(4x + 7 = 43\) (since vertical angles are equal).

Step3: Solve for \(x\)

Subtract 7 from both sides: \(4x = 43 - 7 = 36\).

Divide both sides by 4: \(x = \frac{36}{4} = 9\).

Answer:

9