Question

Two supporting reasons are missing from the proof. Complete the proof by dragging and dropping the appropriate reasons into each of the empty boxes.

Given: m∥n m∠3=120°

Prove: m∠8=60° 



Statements         Reasons
​ m∥nm∠3=120° ​ Given
∠5≅∠3 __________
m∠5=m∠3 Angle Congruence Postulate
m∠5=120° Substitution Property of Equality
m∠8+m∠5=180° Linear Pair Postulate
m∠8+120°=180° ___________
​ m∠8=60° ​ Subtraction Property of Equality 

Answer choices: 

1. Angle Addition Postulate

2. Alternate Interior Angles Theorem

3. Substitution Property of Equality

4. Alternate Exterior Angles Theorem

Answer 1

The reason for ∠5≅∠3 is Alternate Interior Angles Theorem and the reason for ∠8+120°=180° is Substitution Property of Equality.

Explanation:

It is given that the lines m and n are parallel to each other. The measure of angle 3 is 120 degree.

From the figure it noticed that the p is a transversal line intersecting the lines m and n.

According to the Alternate Interior Angles Theorem, if a transversal line intersect two parallel lines then the alternate interior angles are same.

By Alternate Interior Angles Theorem

`\angle 3\cong \angle 5`

`\angle 4\cong \angle 6`

Therefore, the reason for ∠5≅∠3 is Alternate Interior Angles Theorem.

Since the measure of angle 3 is 120 degree.

`\angle 5=120^(\circ)`

The angle 5 and 8 lies on a straight line, so by Linear Pair Postulate,

`\angle 8+\angle 5=180^(\circ)`

Use Substitution Property of Equality and substitute
`\angle 5=120^(\circ)`.

`\angle 8+120^(\circ)=180^(\circ)`

Using Subtraction Property of Equality

`\angle 8=60^(\circ)`

Therefore the reason for ∠8+120°=180° is Substitution Property of Equality.

Answer 2

The answer is alternate interior angles theorem and substitution property of equality.