Question

i really dont understand this. at first i thought you do 2x+5=7x but than i got that the answer is 7 and it doesnt look right at all so here i am. thank you.

Answer 1

- 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:

`\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}`

- Thus, the segment IU is:

`\begin{gathered} IU=7x \\ IU=7*1=7 \end{gathered}`