A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.

Question

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. 
<img src="http://learn.flvs.net/webdav/assessment_images/educator_mjprealgebra_v16/02_07_10.gif" alt="  


Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle) 
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles) 
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p 
Step 4: So, m∠m + m∠n = m∠p

directrix · Answer

Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)

 In this step, the student comes up with 90 degrees from nowhere. In addition, there are no alternate interior angles in the diagram because there are no parallel lines.

directrix · Answer

The proof should go something like this:

 Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)

 Step 2: m∠p + m∠o = 180 degrees (Supplementary Angles)

 Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p (Substitution or Transitive)

 Step 4: So, m∠m + m∠n = m∠p (Subtraction)

directrix · Answer

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