Question

1. find the value of x. show work.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(3x - 22=x + 80\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(3x-x-22=x - x+80\), which simplifies to \(2x-22 = 80\).
Add 22 to both sides: \(2x-22 + 22=80 + 22\), so \(2x=102\).
Divide both sides by 2: \(x=\frac{102}{2}\).

Answer:

\(x = 51\)