Question

How do I find the missing alternative for L2and L3?

Answer 1

Notice that the angles 3 and 4 are supplementary angles, as well as the angles 1 and 2, since both pairs of angles make a straight line (a 180º degree angle).

Then:

`\begin{gathered} m\angle1+m\angle2=180 \\ m\angle3+m\angle4=180 \end{gathered}`

Since the measures of the angles 1 and 4 are given, we can use those equations to find the values of 2 and 3:

`\begin{gathered} 103.4+m\angle2=180 \\ \Rightarrow m\angle2=180-103.4 \\ \Rightarrow m\angle2=76.6 \end{gathered}`
`\begin{gathered} m\angle3+76.6=180 \\ \Rightarrow m\angle3=180-76.6 \\ \Rightarrow m\angle3=103.4 \end{gathered}`

Another way to find the measure of the angles 2 and 3 is to notice that the angles 3 and 1 are alternate interior angles, as well as the angles 2 and 4. The measures of alternate interior angles must be the same, then, the measures of 3 and 1 are 103.º, and the measures of 2 and 4 are 76.6º.

Therefore, the answers are:

`\begin{gathered} \angle2=76.6º \\ \angle3=103.4º \end{gathered}`