To determine which argument is correct, let's review the definitions and logic provided in each argument:

Argument 1:

"If two angles measure $30^\circ$ and $60^\circ$, then the angles are complementary. $\angle 1$ and $\angle 2$ are complementary. So, $m\angle 1 = 30^\circ$ and $m\angle 2 = 60^\circ$."

Analysis:

• Complementary angles are two angles whose measures add up to $90^\circ$.
• Here, it's stated that the angles measure $30^\circ$ and $60^\circ$.
• The sum of $30^\circ + 60^\circ = 90^\circ$, which satisfies the definition of complementary angles.

Argument 2:

"If two angles measure $30^\circ$ and $60^\circ$, then the angles are complementary. The measure of $\angle 1$ is $30^\circ$ and the measure of $\angle 2$ is $60^\circ$. So, $\angle 1$ and $\angle 2$ are complementary."

Analysis:

• This argument also correctly identifies that the sum of $30^\circ$ and $60^\circ$ is $90^\circ$, making the angles complementary.

Both arguments are logically correct as they both correctly identify that angles measuring $30^\circ$ and $60^\circ$ are complementary because their measures add up to $90^\circ$.

Correct Answer:

Both Argument 1 and Argument 2 correctly explain why the angles are complementary.

However, the task may be to select the best explanation format. If that is the case, since Argument 2 explicitly states the measures and concludes the angles are complementary directly, it may be considered slightly clearer.

Let's fill out the required fields based on this reasoning:

Argument 2 is correct. This argument uses the definition of complementary angles.

Would you like further details or have any questions? Here are some related questions:

1. What are the definitions of supplementary and complementary angles?
2. Can two obtuse angles be complementary? Why or why not?
3. How do you determine if two angles are complementary if you know their algebraic expressions?
4. What is the measure of each angle if two complementary angles are equal?
5. How can the concept of complementary angles be applied in solving geometric problems?

Tip: Always verify the sum of the angles when determining if they are complementary or supplementary.