Solution
- The triangle RTU is congruent to triangle RIU.
- This is because both triangles have a common side RU. They also have two equal angles, 19 degrees. Lastly, they also have RT = RI, given in the question.
- Thus, based on the Side-Angle-Side congruency, both triangles are equal.
- Thus, since TU and UI are the corresponding sides of both triangles, we can as well equate them.
- This is done below:
[tex]\begin{gathered} 2x+5=7x \\ \text{ Subtract 2x from both sides} \\ 5=7x-2x \\ 5x=5 \\ \text{ Divide both sides by 5} \\ \\ x=1 \end{gathered}[/tex]
- Thus, the segment IU is:
[tex]\begin{gathered} IU=7x \\ IU=7\times1=7 \end{gathered}[/tex]
