Select the statement that is missing from the proof below showing that vertical angles formed by intersecting lines are congruent.

Statements Reasons
1. ∠ABD and ∠ABC form a linear pair,∠CBE and ∠ABC form a linear pair 1. Definition of a linear pair
2. ∠ABD and ∠ABC are supplementary,∠CBE and ∠ABC are supplementary 2. Linear pair postulate
3. m∠ABD + m∠ABC = 180°,m∠CBE + m∠ABC = 180° 3. Definition of supplementary
4. ? 4. Substitution Property of Equality
5. m∠ABD = m∠CBE 5. Subtraction Property of Equality
6. ∠ABD≅∠CBE 6. Definition of congruent angles

m∠ABD+ m∠ABC = m∠DBC

m∠ABD+m∠DBE = m∠ABE

m∠ABD+m∠ABC=m∠DBE+m∠EBC

m∠ABD+ m∠ABC = m∠CBE + m∠ABC

The proof is given, but a step is missing to be chosen from the option that best suits the options which showing that vertical angles formed by intersecting lines are congruent.

What is the angle?

The angle can be defined as the one line inclined over another line.

From statement 3, m∠ABD + m∠ABC = 180°,m∠CBE + m∠ABC = 180° 3. Definition of supplementary. in the statement
m∠ABD + m∠ABC = 180° - - - -(1)
m∠CBE + m∠ABC = 180° - - - -(2)

Equating both equations 1 and 2
m∠ABD + m∠ABC = m∠CBE + m∠ABC

So next step is m∠ABD+ m∠ABC = m∠CBE + m∠ABC because the Substitution Property of Equality.

Thus, m∠ABD+ m∠ABC = m∠CBE + m∠ABC is required 4th step best suitable in the proof.

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