Question

1. is this a valid argument? given: if the sum of the measure of two angles equals 90°, then the angles are complementary. the sum of the measures of ∠a and ∠b is 90° conclusion: ∠a and ∠b are complementary. no. this is an improper use of the law of detachment. yes. this argument uses the law of detachment. yes. this argument uses the law of syllogism. no. this is an improper use of the law of syllogism.

Explanation:

The Law of Detachment states that if a conditional statement \( p \to q \) is true and \( p \) is true, then \( q \) is true. Here, the conditional is "If the sum of two angles is \( 90^\circ \) ( \( p \) ), then they are complementary ( \( q \) )". We know the sum of \( \angle A \) and \( \angle B \) is \( 90^\circ \) ( \( p \) is true), so by Law of Detachment, \( q \) (they are complementary) follows. The Law of Syllogism involves two conditionals to form a new conditional, which is not the case here. So the argument is valid and uses Law of Detachment.

Answer:

B. Yes. This argument uses the Law of Detachment.