Question

by the definition of suplementary angles Angle 1+angle 2=______and angle 2+angle 3=_______ than angle 1+ angle 2+ angle 3 by the ______. Subtract angle 2 from each side. You get Angle 1=_____

Answer 1

By the definition of supplementary angles, angle 1 + angle 2 = 180° and angle 2 + angle 3 = 180°. Then angle 1 + angle 2 = angle 2 + angle 3 = 180°. Subtract angle 2 from each side. You get angle 1 = angle 3, or angle 1 ≅ angle 3.

Explanation:

The Complete/Correct Question Reads:

By the definition of supplementary angles, angle 1 + angle 2 = _____ and angle 2 + angle 3 = ____ . Then angle 1 + angle 2 = angle 2 + angle 3 ______. Subtract angle 2 from each side. You get angle 1 = ______, or angle 1 ≅ ______.

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By definition we know that if the Sum of Two Angles is Equal to 180° then the angles are Supplementary.

Now looking at the schematic we can see that our Supplementary angle pairs are:

• 
  `m`∠1 and
  `m`∠2

• 
  `m`∠3 and
  `m`∠2

So let us start solving.

`m`∠1
`+`
`m`∠2
`= 180^(o)`

`m`∠3
`+`
`m`∠2
`=180^(o)`

Then, we have

`m`∠1
`+`
`m`∠2 =
`m`∠3
`+`
`m`∠2
`=180^(o)`

So subtracting
`m`∠2 from each side we have:

`m`∠1
`+`
`m`∠2
`-`
`m`∠2 =
`m`∠3
`+`
`m`∠2
`-`
`m`∠2

`m`∠1
`=`
`m`∠3 OR
`m`∠1 ≅
`m`∠3

So your paragraph will be:

By the definition of supplementary angles, angle 1 + angle 2 = 180° and angle 2 + angle 3 = 180°. Then angle 1 + angle 2 = angle 2 + angle 3 = 180°. Subtract angle 2 from each side. You get angle 1 = angle 3, or angle 1 ≅ angle 3.