Question

part 4 of 7
write a two-column proof for the following.
given: m∠2 = 30
m∠1 = 2m∠2
prove: m∠3 + m∠4 = 90
(do not include the degree symbol in your answers.)
statements reasons

1. m∠2 = 30 1) given
2. m∠1 = 2m∠2 2) given
3. m∠1 = 2(30) 3) substitution
4. m∠1 = 60 4) simplification
5. m∠3 = 30 5) vertical angles theorem
6. m∠3 + m∠4 = 30 + m∠4 6) dropdown

diagram of intersecting lines with angles 1,2,3,4

Explanation:

Step1: Identify the operation

In step 6, we substitute \( m\angle3 = 30 \) into \( m\angle3 + m\angle4 \). This is the Substitution Property of Equality, which states that if \( a = b \), then \( a + c = b + c \) (in this case, \( c = m\angle4 \), \( a = m\angle3 \), \( b = 30 \)).

Step2: Determine the reason

The reason for \( m\angle3 + m\angle4 = 30 + m\angle4 \) is the Substitution Property (since we substitute the known value of \( m\angle3 \) into the expression).

Answer:

Substitution Property (or Substitution)