Angie is incorrect. The statement "irrational numbers are real numbers" is always true.
Irrational numbers are a subset of real numbers. Real numbers include both rational numbers (like \( \frac{1}{2} \) or 3) and irrational numbers (like \( \sqrt{2} \) or \( \pi \)).
For example, the number \( \sqrt{2} \) is an irrational number, and it is also a real number. Therefore, it is correct to say that irrational numbers are real numbers.