Question

intersecting lines r, s, and t are shown below. what is the value of x?

Explanation:

Step1: Use vertical - angle property

The angle vertical to the \(106^{\circ}\) angle is also \(106^{\circ}\).

Step2: Apply exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So \(106^{\circ}=x + 23^{\circ}\).

Step3: Solve for \(x\)

Subtract \(23^{\circ}\) from both sides of the equation: \(x=106^{\circ}- 23^{\circ}\).

Answer:

\(83\)