Adam and darius provide the following proofs for vertical angles to be equal: adam's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360° therefore, angle 2 + angle 3 = 180° (t is a straight line) hence, angle 1 = angle 3 (transitive property of equality) darius' proof: angle 1 + angle 4 = 180° (t is a straight line) angle 1 + angle 2 = 180° (pq is a straight line) therefore, angle 1 + angle 2 = angle 1 + angle 4 (transitive property of equality) hence, angle 2 = angle 4 (subtraction property of equality) which statement is correct?

Answer with explanation:

Proof Provided by Adam for vertical angles to be equal:

 The Sum of Angles in Complete Circle is 180°.

So,∠1 + ∠2 +∠3+∠4=360°

∠2+∠3=180°------[t is a straight line]

∠1 + 180°+∠4=360°

∠1+∠4=360° -180°

Also, ∠1 +∠4=180°

But, Here it is given that,

∠1 = ∠ 3

⇒Incorrect proof Done by Adam

⇒Proof Provided by Darius for vertical angles to be equal:

  ∠1 + ∠4=180°------(t is a straight line)-----(1)

Also, ∠1 + ∠2=180°------(P Q is a straight line)-----(2)

From (1) and (2)

⇒∠1 + ∠4=∠1 + ∠2→→→(Transitive Property of Equality)

⇒ ∠4=∠2→→→(Subtraction Property of Equality)

Correct Proof done by Darius