B. The error is in step 4, where the equation m∠5 + m∠6 = 180° should be obtained by the angle addition postulate. The correction is to replace step 4 with the following:
By the angle addition postulate, m∠1 + m∠5 = m∠5 + m∠6.
By subtracting m∠5 from both sides, we have m∠1 = m∠6.
So, by the definition of supplementary angles, ∠1 and ∠6 are supplementary.
Prove: ∠1 and ∠6 are supplementary.
Proof:
Since parallel lines make corresponding angles congruent, ∠1 ≅ ∠5.
By the definition of congruence, m∠1 = m∠5.
By the defintion of a linear pair, ∠5 and ∠6 are a linear pair and are supplementary.
By the definition of supplementary angles, m∠5 + m∠6 = 180°.
Applying the symmetric property, m∠1 + m∠6 = 180°.
So, by the definition of supplementary angles, ∠1 and ∠6 are supplementary.
In which step was the error made and how should the error be corrected?
A.
The error is in step 5, where the equation m∠1 + m∠6 = 180° should be obtained by the substitution property.
B.
The error is in step 4, where the equation m∠5 + m∠6 = 180° should be obtained by the angle addition postulate.
C.
The error is in step 1, where ∠1 ≅ ∠5 should be true because parallel lines make alternate interior angles congruent.
D.
The error is in step 3, where ∠5 and ∠6 are vertical angles and should be supplementary because of the definition of vertical angles.
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