Question

A pair of parallel lines is cut by a transversals: What is the measure of angle x?A) 25 degrees B) 40 degrees C) 55 degrees D) 105 degrees

Answer 1

Alternate interior angles are those pairs of non-adjacent angles that are located between the parallel lines. These are located on opposite sides of the transversal.

Alternate interior angles are congruent, which means that they have equal measure.

Analizing the picture given in the exercise, you can identify that the angle that measures 80 degrees and the angle obtained by adding the other two angles indicated in the figure, are Alternate interior angles.

Then, you can set up the following equation:

`x+25\degree=80\degree`

Now you must solve for "x":

`\begin{gathered} x=80\degree-25\degree \\ x=55\degree \end{gathered}`

The answer is: Option C.