Question

1. find the value of x.

(4x - 101)°
(2x + 3)°
options: 46, 31, 107, 52

Explanation:

Step1: Identify Vertical Angles

The angles \((4x - 101)^\circ\) and \((2x + 3)^\circ\) are vertical angles, so they are equal.
\[4x - 101 = 2x + 3\]

Step2: Solve for \(x\)

Subtract \(2x\) from both sides:
\[4x - 2x - 101 = 3\]
\[2x - 101 = 3\]

Add 101 to both sides:
\[2x = 3 + 101\]
\[2x = 104\]

Divide both sides by 2:
\[x = \frac{104}{2}\]
\[x = 52\]

Answer:

52