Question

for the image below, answer the following questions.
a) what are the angle pair?
b) find the value of x.
(image shows two intersecting lines with one angle labeled 78° and another labeled (5x - 2)°)

Explanation:

Step1: Identify the angle pair

The given angles \(78^{\circ}\) and \((5x - 2)^{\circ}\) are vertical angles. Vertical angles are equal.

Step2: Set up the equation

Since vertical angles are equal, we have the equation \(5x-2 = 78\).

Step3: Solve for \(x\)

Add \(2\) to both sides of the equation: \(5x-2 + 2=78 + 2\), which simplifies to \(5x=80\).
Divide both sides by \(5\): \(x=\frac{80}{5}\).

Answer:

a) Vertical angles
b) \(x = 16\)