To answer this question we will use that alternate interior angles ( for parallel lines) are congruent and that the interior angles of a triangle add up to 180 degrees.
Using the fact that the interior angles of a triangle add up to 180 degrees, we can set the following equation:
[tex]\measuredangle10+\measuredangle9+\measuredangle6=180^{\circ}.[/tex]
Now, since a||b and angles 9 and 1 are alternate interior angles then:
[tex]\measuredangle9\cong\measuredangle1,[/tex]
Therefore:
[tex]\measuredangle9=9x-20.[/tex]
Substituting
[tex]\begin{gathered} \measuredangle9=9x-20, \\ \measuredangle6=2x+6, \\ \measuredangle10=5x-10, \end{gathered}[/tex]
in the first equation we get:
[tex]9x-20+2x+6+5x-10=180.[/tex]
Solving for x we get:
[tex]\begin{gathered} 16x-24=180, \\ 16x=204, \\ x=12.75. \end{gathered}[/tex]
Answer: Option C.
