Both arguments starts out with a true conditional statement. How do the arguments differ in the next two sentences?
Argument 2, see solution.
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Both arguments starts out with a true conditional statement.
If two angles measure $30^(∘)$ and $60^(∘)$,
then the angles are complementary.
In the next two sentences, the arguments differ.
Argument 1
If we rewrite the second and third sentence into a conditional statement, we see that it is actually (although more specific) the converse of the first conditional statement.
If $∠1$ and $∠2$ are complementary,
then $m∠1=30^(∘)$ and $m∠2=60^(∘)$.
This is not a true conditional statement, as complementary angles do not have to be 30^(∘) and 60^(∘). They could be any other measures as long as they have a sum of 90^(∘).
Argument 2
If we rewrite the second and third sentence into a conditional statement, we see that it is the same conditional statement as the first one.
If $∠1=30^(∘)$ and $∠2=60^(∘)$
then $∠1$ and $∠2$ are complementary.
Since the original conditional statement is true, this one must be as well. Therefore, Argument 2 is the correct answer.
