Question

1. error analysis jayden states that based on the congruent supplements theorem, if m∠1 + m∠2 = 90 and if m∠1 + m∠3 = 90, then ∠2 ≅ ∠3. what is the error in jayden’s reasoning? © mp.3

Explanation:

Step1: Recall the Congruent Supplements Theorem

The Congruent Supplements Theorem states that if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. Supplements mean the sum of two angles is 180 degrees.

Step2: Analyze Jayden's given equations

Jayden has \(m\angle1 + m\angle2=90\) and \(m\angle1 + m\angle3 = 90\). These are sums that equal 90 degrees, which means \(\angle1\) and \(\angle2\) are complementary, and \(\angle1\) and \(\angle3\) are complementary.

Step3: Identify the error

The error is that Jayden is applying the Congruent Supplements Theorem when the angles are complementary (sum to 90 degrees) instead of supplementary (sum to 180 degrees).

Answer:

Jayden is mis - applying the Congruent Supplements Theorem. The theorem applies to supplementary angles (sum to 180 degrees), but the given angle - pairs are complementary (sum to 90 degrees).