Question

I need help sorry for bothering everyone. 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∥nm∠2=60° Prove: m∠7=120

Answer 1

since ∠2=60° = ∠8 so it will also be 60 °
the sum of the both are 60°+∠7=180°
∠7= 180°- 60° = 120°

Answer 2

Given:

`m \parallel n\\m\angle 2 = 60\°`

Prove:

`m\angle 7 = 120\°`

1.
`m \parallel n\\m\angle 2 = 60\°` , by Given.

2.
`m\angle 2 = m\angle 8`, by Alternate Exterior Angles Theorem.

3.
`m\angle 8= 60\°`, by substitution.

4.
`m\angle 8 + m\angle 7 = 180\°`, by Straight Angle Definition and Supplementary Angle Theorem.

5.
`60\° +m\angle 7 = 180\°\\m\angle 7= 180\° - 60\°\\m\angle 7= 120\°`, by substitution.

`\therefore m\angle 7 = 120\°`

It's important to remember that Alternate Exterior Angles are those which are placed outside the parallels and at different sides of the transversal, and these angles are always congruent.

Additionally, the definition of a straight angle is that this angle is equal to 180°, and supplementary angles theorem states that adjacent angles that sum 180° are supplementary one each other.