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 w. The angle adjacent to w is marked as z, and the other two angles inside the triangle are marked as x and y.
Step 1: m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)
Step 2: m∠w − m∠z = 90 degrees (corresponding angles)
Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z
Step 4: So, m∠x + m∠y = m∠w
In which step did the student first make a mistake and how can it be corrected? (5 points)
a
Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of corresponding angles)
b
Step 2; it should be m∠w + m∠z = 180 degrees (supplementary angles)
c
Step 1; it should be m∠x + m∠y + m∠z = 90 degrees (corresponding angles)
d
Step 2; it should be m∠w + m∠z = 90 degrees (alternate exterior angle)
Answers
Given : A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC is equal to the measure of the exterior angle
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∠p = 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∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
To Find : 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 = 180 degrees (sum of angles in a triangle)
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; m∠p − m∠o = 90 degrees (alternate interior angles)
Solution :
option a) is correct
student first make a mistake in 1st step.
Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
∠p is exterior angle he used ∠p instead of ∠o
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∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
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Answer:
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Given : A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC is equal to the measure of the exterior angle
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∠p = 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∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
To Find : 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 = 180 degrees (sum of angles in a triangle)
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; m∠p − m∠o = 90 degrees (alternate interior angles)
Solution :
student first make a mistake in 1st step.
Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
∠p is exterior angle he used ∠p instead of ∠o
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∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
Step-by-step explanation: