Question

Complete the proof. help me answer this please!!

Answer 1

2. Definition of supplementary angles

3.
`\angle 1 + \angle 2 = \angle 1 + \angle 3`

4.
`\angle 2 = \angle 3`

5. Definition of congruent angles

Explanation:

Required

Fill in the gaps

1. Given

Supplementary angles:
`\angle 1` and
`\angle 2`

Supplementary angles:
`\angle 1` and
`\angle 3`

2. Supplementary angles add up to 180.

So:

`\angle 1 + \angle 2 = 180`

`\angle 1 + \angle 3 = 180`

3. Apply transitive property on (2)

`\angle 1 + \angle 2 = 180` and
`\angle 1 + \angle 3 = 180`, then

`\angle 1 + \angle 2 = \angle 1 + \angle 3`

4. Subtract
`\angle 1` from both sides

`\angle 1 - \angle 1 + \angle 2 = \angle 1 + \angle 3 - \angle 1`

`\angle 1 - \angle 1 + \angle 2 = \angle 1 - \angle 1+ \angle 3`

`\angle 2 = \angle 3`

This property is called the subtraction property

5. If
`\angle 2 = \angle 3`,

Then
`\angle 2` and
`\angle 3` are congruent