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?

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

D

Explanation:

Steo 2 It should be m < o + m < p = 180 degrees

Answer 2

D. Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)

Explanation:

Consider the provided figure.

Two Angles are known as Supplementary if the sum of them is 180 degrees.

Alternate Exterior Angles: It is the pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

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

Step 4:

So, m∠m + m∠n = m∠p

By comparing the provided options with above steps we can concluded that the correct option is D.

D. Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles).