Katherine wants to prove that the measures of the interior angles of a triangle have a sum of 180' She draws a triangle and extends one of the sides through a vertex. She then draws a line through th Vertex thai paralel to the opposite side as shown in the diagram below

The statements that must be true are;

A. m∠1 = m∠5

B. m∠2 = m∠4

C. m∠3 + m∠4 + m∠5 = 180°

Step-by-step explanation:

The given parameters are;

The fact Katherine wants to prove = The sum of the measures of the interior angles of a triangle  = 180°

The line Katherine drew passing through the vertex = Parallel to the opposite side of the triangle

Therefore we have;

1) m∠1 and m∠5 are corresponding angles and m∠1 = m∠5 for corresponding angles of parallel lines having the same transversal

2) m∠2 and m∠4 are alternate interior angles and m∠2 = m∠4 for alternate interior angles of parallel lines having the same transversal

3) m∠3 and m∠4 and m∠5 are angles on a straight line and angles on a straight line are supplementary

∴ m∠3 + m∠4 + m∠5 = 180°, by the definition of supplementary angles

Therefore, m∠3 + m∠2 + m∠1 = 180° (substitution property)

m∠3 + m∠2 + m∠1 = Sum of interior angles of a triangle = 180°.