Question

if two angles are complementary angles, the sum of the measures of the angles is 90°. ∠1 and ∠2 are complementary angles. what conclusion can be drawn from the given statements and why? choose the correct answer. a) the sum of the measures of ∠1 and ∠2 is 90° by the law of detachment. b) the sum of the measures of ∠1 and ∠2 is 90° by the law of syllogism. c) the sum of the measures of ∠1 and ∠2 is 180° by the law of syllogism. d) no valid conclusion can be drawn. the given statements are not related in a way that allows either law to apply.

Explanation:

Step1: Identify the conditional statement

The statement "If two angles are complementary angles, the sum of the measures of the angles is 90°" is a conditional statement (if - then statement).

Step2: Identify the hypothesis - conclusion match

We are given that ∠1 and ∠2 are complementary angles. This matches the hypothesis of the conditional statement. By the law of Detachment, if the hypothesis of a true conditional statement is true, then the conclusion is true. So the sum of the measures of ∠1 and ∠2 is 90°.

Answer:

A. The sum of the measures of ∠1 and ∠2 is 90° by the law of Detachment.