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.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior 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?
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)

Answer 1

The student made the mistake in Step 2.

It should be m∠o + m∠p = 180 (Supplementary angles)

If this is corrected, then, since m∠m + m∠n + m∠o = 180 from Step 1,

we have,

m∠m + m∠n + m∠o = m∠o + m∠p which is Step 3.

Cancelling m∠o both sides, we get,

m∠m + m∠n = m∠p which is Step 4.