The triangle angle sum theorem states that sumof interior angles in a triangle equals 180 degrees.
Here the interior angles are ∠3, ∠4, and ∠5.
To prove that m∠3 + m∠4 + m∠5 = 180 degrees, we have the following:
∠1 and ∠2 and ∠3 from line CP: Definition of a straight angle
m∠1 + m∠2 + m∠3 = 180 degrees: Substitution
Line CP is parallel to line AB: Given
∠1 ≅ ∠4, ∠2 ≅ ∠5: If two parallel lines are cut by a transversal, alternate interior angles are congruent.
m∠1 = m∠4, m∠2 = m∠5: Definition of congruence
m∠4 + m∠5 + m∠3: = 180 degrees: Commutative property
m∠3 + m∠4 + m∠5 = 180 degrees: Angle Addition Postulate