Answer: x = 18
Concept:
Here, we need to know the idea of the isosceles decomposition theorem.
The Isosceles Decomposition Theorem states that in an isosceles triangle if a line segment goes from the vertex angle to the base, the following conditions are equivalent:
-
The line segment meets the base at its midpoint,
- The line segment is perpendicular to the base.
- The line segment bisects the vertex angle.
In this question, the first condition that is equivalent would be useful.
Solve:
Given information
First side of the line segment (TU) = 2x + 24
Second side of the line segment (UR) = 5x - 30
Given expression deducted from the first condition of the isosceles decomposition theorem
Second side = First side
Substitute values into the expression
5x - 30 = 2x + 24
Add 30 on both sides
5x - 30 + 30 = 2x + 24 + 30
5x = 2x + 54
Subtract 2x on both sides
5x - 2x = 2x + 54 - 2x
3x = 54
Divide 3 on both sides
3x / 3 = 54 / 3
[tex]\boxed{x=18}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
