Questions: Find the value of x.

Solution Steps

Since two sides of the triangle inside the circle have lengths of 12 and meet at a 90° angle, the triangle must be inscribed in a semicircle. This means the third side of this triangle is the diameter of the circle, and has a length of 12√2 (by the Pythagorean theorem: a² + b² = c² => 12² + 12² = c² => 144 + 144 = c² => 288 = c² => c = √288 => c = √(144 * 2) => c = 12√2 ). Therefore, the radius of the circle is (12√2)/2 = 6√2.

Two sides of the triangle containing the angle x have length 6√2 (the radius). The third side also has length 6√2 because it is marked congruent to one of the radii. Since all sides are congruent, it must be an equilateral triangle.

All angles in an equilateral triangle are 60°. Therefore, x = 60°

Final Answer: The final answer is $\boxed{60}$