GIVEN
Two triangles ABC and ACD where two corresponding sides of the two triangles are equal.
SOLUTION
The two triangles have equal sides such that:
[tex]\begin{gathered} AB=AD \\ and \\ AC=AC \end{gathered}[/tex]
By this, the length of the remaining sides BC and DC are related such that the side opposite the greater angle has the greater length.
Since [tex]BC>DC[/tex]Substitute known values into the inequality:
[tex]\begin{gathered} DC=11x-33 \\ BC=77 \\ \therefore \\ 77>11x-33 \end{gathered}[/tex]
Solving the inequality:
[tex]\:x<10[/tex]
Recall that the side DC has to be greater than 0. Therefore:
[tex]\begin{gathered} 11x-33>0 \\ \therefore \\ x>3 \end{gathered}[/tex]
Combining both solutions:
[tex]3
ANSWER
