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)
I know its one of the step two answers but which one?

Answer 1

Given steps  :

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) : It's incorrect step because m<p and m<0 are on a common point on a line and make a linear pair. Therefore, m<p and m<0 are supplementary angles.

Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p.

Step 4: So, m∠m + m∠n = m∠p.

Therefore, student did mistake in 2nd step and correct step should be  Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles).