Question

Help please! I'm just uncertain about what d is.

Complete the paragraph proof.

Given: angle 1 and angle 2 are supplementary, and angle 2 and angle 3 are supplementary.

Prove: angle 1 ≅ angle 3

By the definition of supplementary angles, angle 1 + angle 2 = _____(a) and angle 2 + angle 3 = ____ (b). Then angle one + angle 2 = angle 2 + angle 3 ______(c). Subtract angle 2 from each side. You get angle 1 = ______(d), or angle 1 ≅ ______(e).

I think that they are the following.

a is 180 degrees.
b is 180 degrees.
c is 360 degrees.
d ???
e is angle 3

What do you think d is? Do you think I am correct?

Answer 1

Part a)
`180\°`

Part b)
`180\°`

Part c)
`180\°`

Part d) Angle
`3`

Part e) Angle
`3`

Explanation:

we know that

If two angles are supplementary

then

their sum is equal to
`180\°`

In this problem

angle 1 and angle 2 are supplementary, and angle 2 and angle 3 are supplementary

so

`m<1+m<2=180\°` --------> equation A

`m<2+m<3=180\°` --------> equation B

equate equation A and equation B

`m<1+m<2=m<2+m<3`

Subtract
`m<2` both sides

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

`m<1=m<3`

therefore

m<1≅m<3

Answer 2

By the definition of supplementary angles,
a. angle 1 + angle 2 = 180 degrees
b. and angle 2 + angle 3 = 180 degrees
c. Then angle one + angle 2 = angle 2 + angle 3 = 180 degrees
d. Subtract angle 2 from each side. You get angle 1 = angle 3
e. or angle 1 ≅ angle 3

I hope that the above answer is absolutely clear to you.