Question

Question #076ff

Answer 1

I tried this:

Explanation:

Ok...basically angle 5 and 6 are the same and adding angle 4 and 6 you shoulfd get `180^@`....
If you look at, say, angle 5, I would say that is `90^@+"something"`
Let us call this something `x`, so:
angle 5=angle 6 = `90^@+x`
as a consequence: angle 4 = `90^@-x`

From the supplementary condition we want that:

angle 4 + angle 6 = `180^@`

let us substitute our first guesses for the two angles (4 and 6):

`(90^@-x)+(90^@+x)=180^@`
rearranging:
`90^@cancel(-x)+90^@cancel(+x)=180^@`
which is true!

Does it make sense?

Answer 2

Given `/_5~=/_6`
and
from the figure it is evident that `" "/_4 and /_5"` are adjacent angles formed due to standing of one line segment on other.

So `/_4 + /_5=180^@->" supplementary"`

`=>/_4 + /_6=180^@->" supplementary"`

PROVED

(Replacing `/_5" by "/_6" as they are congruent"`)

Answer 3

I tried this to include a Starement/Reason set up:

Explanation:

I came out with...this: