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.
http://assets.openstudy.com/updates/attachments/5581b5e7e4b07028ea60ea91-ticklemepickle-1434564169139-02_07_10.gif

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

In which step did the student first make a mistake and how can it be corrected?

Answer 1

A) Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
B) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
C) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
D) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)

Answer 2

Hmm what do you think? :)

Answer 3

Hint:
The red angles are the angles of a triangle, so they add to 180.
The blue angles are adjacent angles, so they add to 180.