In order to solve for x, first let's find the vertical angle to the given angle of 83°.
Vertical angles are congruent, therefore the vertical angle also measures 83°.
Now, comparing angle x and the vertical angle we found, they are consecutive interior angles, therefore they are supplementary angles.
Supplementary angles have a sum equal to 180°, so we have:
[tex]\begin{gathered} 83+x=180 \\ x=180-83 \\ x=97° \end{gathered}[/tex]
Angle mthe measure of m
