Question

1. error analysis what error did tyler make?

m∠1 = 72 by same - side exterior angles theorem

1. generalize in the diagram shown, if x + y = 180,

Explanation:

Step1: Identify the correct theorem

The Same - Side Exterior Angles Theorem states that same - side exterior angles are supplementary (their sum is \(180^{\circ}\)), not equal. The angle of \(72^{\circ}\) and \(\angle1\) are same - side exterior angles. So the correct relationship is \(m\angle1+ 72^{\circ}=180^{\circ}\).

Step2: Calculate \(m\angle1\)

Using the supplementary angle relationship, we have \(m\angle1 = 180^{\circ}- 72^{\circ}\)
\(m\angle1=108^{\circ}\)
The error is that the Same - Side Exterior Angles Theorem was misapplied. Same - side exterior angles are supplementary, not congruent (equal). So the mistake was assuming that same - side exterior angles are equal (using a wrong theorem application) instead of recognizing they are supplementary.

Answer:

The error is misapplying the Same - Side Exterior Angles Theorem. Same - side exterior angles are supplementary (sum to \(180^{\circ}\)), not equal. So \(m\angle1\) should be \(180^{\circ}-72^{\circ} = 108^{\circ}\), not \(72^{\circ}\).