Question 2 (Worth 4 points)

(02.07)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 = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠n + 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 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p

Step 2; it should be m∠o − m∠p = 90 degrees (complementary angles)

Points earned on this question: 4

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Respuesta :

wagonbelleville wagonbelleville · Answer 1 · 2019-03-14T06:33:50+01:00

Answer:

Step 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p

Step-by-step explanation:

We are given that,

Triangle ABC having three interior angles ∠m, ∠n and ∠o and an exterior angle ∠p.

It is required to prove m∠m + m∠n = m∠p

Now, according to the steps shown by the student, we see that,

From step 1, we have, m∠m + m∠n + m∠o = 180°

From step 2, we have, m∠p + m∠o = 180°

Thus, in step 3, we get, m∠m + m∠n + m∠o = m∠p + m∠o.

But, the student did m∠m + m∠n + m∠o = m∠p + m∠n, which is wrong.

Thus, the student made the mistake in step 3 as the relation should be m∠m + m∠n + m∠o = m∠p + m∠o.