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olganol [36]
3 years ago
8

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b

elow 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 w 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? 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 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Mathematics
2 answers:
blagie [28]3 years ago
7 0
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)
astraxan [27]3 years ago
4 0

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

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