Question

what is the value of x?
triangle t r s with side t r labeled 10, side t s labeled x. angles at r and s are marked equal (with red arcs).
x = blank box

Explanation:

Step1: Identify Triangle Type

The triangle \( \triangle TRS \) has two equal angles (at \( R \) and \( S \)), so it's isosceles.

Step2: Apply Isosceles Triangle Property

In an isosceles triangle, sides opposite equal angles are equal. Side \( TR = 10 \) is opposite \( \angle S \), and side \( TS = x \) is opposite \( \angle R \). Since \( \angle R=\angle S \), \( TS = TR \).

Answer:

\( x = 10 \)