Joel and melinda provide the following proofs for vertical angles to be equal:

joel's proof: angle 2 + angle 3=180° (t is a straight line)
angle 1 + angle 2 = 180° (pq is a straight line)
therefore, angle 1 + angle 2 = angle 2 + angle 3 (transitive property of equality)
hence, angle 1 = angle 3 (subtraction property of equality)

melinda's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
therefore, angle 1 + angle 4 = 180° (t is a straight line)
hence, angle 4 = angle 2 (transitive property of equality)

which statement is correct?
a joels is correct
b melindas is correct
c both melinda and joels is correct
d neither is correct

Vertical angles are two opposite angles between two intersecting lines. Based on the following statements, Joel is correct and Melinda is quite wrong.

Let's discuss Joel's first. It is clear from the picture than line t and line PQ are straight lines. So the first two statements are true. Transitive property is illustrated as, if a=b and c=b, then a=c. Since angles 1+2 and angles 2+3 are each equal to 180, then these sum of angles are then equal. Subtraction property of equality is illustrated as, if a-c=d and b-c=d, then a=b. Hence,it applies. The proof is correct.

For Melinda's solution, the logic is missing after the statement: Therefore, angle 1 + angle 4 = 180° (t is a straight line). There must be additional proofs before she could use the transitive property of equality.

Therefore, the answer is letter A.

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