Question

• 2-1: exit ticket

which of the following is the correct set up for an equation that solves for x?
105°
x + 112
105 + x + 112 = 180
105 + x = 112
180-(x + 112)=105
105 = x + 112

Explanation:

Step1: Identify angle - relationship

The two angles \(105^{\circ}\) and \(x + 112^{\circ}\) are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary, meaning their sum is \(180^{\circ}\).

Step2: Set up the equation

We know that \(105+(x + 112)=180\), which can also be rewritten as \(180-(x + 112)=105\) by subtracting \((x + 112)\) from both sides of the equation \(105+(x + 112)=180\).

Answer:

\(180-(x + 112)=105\)