Question

Below is a two-column proof incorrectly proving that the three angles of ΔPQR add up to 180°:

Answer 1

Answer:

Option (A).

Step-by-step explanation:

                         Statements                                   Reasons

1). Draw a line ZY parallel to PQ             1).Construction

2). m∠ZRP + m∠PRQ + m∠QRY = 180°   2). Angle addition postulate

3). ∠ZRP ≅ ∠RPQ                                     3). Alternate interior angles theorem

4). ∠QRY ≅ ∠PQR                                     4). Alternate angle theorem

5). m∠RPQ + m∠PRQ + m∠PQR =m∠ZRY  5). Substitution

6). m∠ZRY = 180°                                     6). Definition of supplementary angles

7). m∠RPQ+m∠PRQ+m∠PQR = 180°       7). Substitution

Here reason of statement (6) is incorrect.

m∠ZRY = 180°, because angle ZRY is a straight angle not a supplementary angle.

Therefore, Option (A) will be the answer.