Vertical angles are congruent.
From the figure, angle 3 and angle (7x + 3) are vertical angles, therefore angle 3 is (7x + 3)
Angle 1 and 127 degrees are supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle1+127=180 \\ \angle1=180-127 \\ \angle1=53 \end{gathered}[/tex]
Angle 2 and 133 degrees are also supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle2+133=180 \\ \angle2=180-133 \\ \angle2=47 \end{gathered}[/tex]
Now we have angles 1, 2 and 3 which are angles in a triangle, and the sum of interior angles in a triangle is 180 degrees.
[tex]\begin{gathered} \angle1+\angle2+\angle3=180 \\ 53+47+(7x+3)=180 \\ \text{Solve for x :} \\ 100+7x+3=180 \\ 7x+103=180 \\ 7x=180-103 \\ 7x=77 \\ x=\frac{77}{7} \\ x=11 \end{gathered}[/tex]
ANSWER :
x = 11
