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.

A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and

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

Answer 1

@iambatman @ChantySquirrel1129** @HS_CA

Answer 2

@CandyCove @Christian_10_

Answer 3

Do you have a picture of the triangle? c:

Answer 4

Diagram

Answer 5

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.

Answer 6

@HELPMEPLZ!!

Answer 7

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)

Answer 8

o+p =180 (linear pair)
o =180-p---------I
m+n+o =180 (sum of the angles in a triangle)
m+n+180-p =180 (from ---I)
m+n - 180 -180 +p
m+n =p
p= m+n
exterior angle at p = sum of interior opposite angles