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 the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.


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? (4 points)

a
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)

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; it should be m∠o + m∠p = 180 degrees (supplementary angles)

Answer 1

C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)

Explanation:

The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)

Hope this helps