Question

In the diagram shown, lines m and n are parallel and crossed by transversal line r. This creates an angle that measures 135º as shown. If the measure of angle 1 is given by the expression 4x - 3 then solve for the value of x.

Answer 1

Given the information in the picture, we have that the angle 135° is corresponding angle with the supplement of angle 1. This is:

Then, since the angle that measures 135° and angle 1 are supplemetary, we have the following:

$\begin{gathered} \measuredangle1=4x-3 \\ \measuredangle1+135=180 \\ \Rightarrow4x-3+135=180 \\ \Rightarrow4x=180+3-135=48 \\ \Rightarrow x=\frac{48}{4}=12 \\ x=12 \end{gathered}$

therefore, x=12