Question

m\angle 1 = 120^\circ

prove
m\angle 3 = 120^\circ

statement reason

1. \angle 1 and \angle 2 form a linear pair 1) given
2. m\angle 1 + m\angle 2 = 180^\circ 2) linear pair postulate
3. \angle 2 and \angle 3 form a linear pair 3) given
4. m\angle 2 + m\angle 3 = 180^\circ 4) linear pair postulate
5. m\angle 1 + m\angle 2 = m\angle 2 + m\angle 3 5) substitution property
6. m\angle 1 = m\angle 3 6) ?
7. m\angle 1 = 120^\circ 7) given
8. 120^\circ = m\angle 3 8) substitution property

Explanation:

Analyze the transition from step 5 to step 6

Using the Geometric Proof knowledge point
We are given the equation in step 5:

$$m\angle1 + m\angle2 = m\angle2 + m\angle3$$

In step 6, the equation becomes:

$$m\angle1 = m\angle3$$

Identify the algebraic property applied

Using the Subtraction Property of Equality knowledge point

$$
LATEXBLOCK0
$$

Answer:

1. <blank>Subtraction Property of Equality</blank>