Question

prove: an exterior angle is greater than or equal to the sum of two remote interior angles.

Answer 1

use hyerbolic

Answer 2

hyperbolic geometry?

Answer 3

sum up all the angles inside the triangle to add up to 180 and sum up the exterior angle with its supplement to add up to 180. You can then solve using simultaneous equations.

Answer 4

yeah

Answer 5

how is it greater than though

Answer 6

lol @Boblovesmath Not quite, but your answer is REALLY close.
Do remember that we're working with *hyperbolic* geometry here, not Euclidean ^_^

Answer 7

Although do follow Bob's lead, @fiberdust
Remember, that the sum of the interior angles of a triangle in the hyperbolic plane is less than 180 degrees.
That's ALL we know about it, but all we need ;)

Answer 8

@terenzreignz I have never had it so you guys can have fun!

Answer 9

Don't worry Bob, you had the right idea.

And here's what triangles sorta look like in the hyperbolic plane:


that triangle in the middle :)

Answer 10

so if i have m<1 as an exterior angle + m< 2 =180 by supplementary axiom and m< 2 +m<3 +m<4 is less than equal to 180 by triangle sum . would this be the start

Answer 11

Precisely.
Much like what Bob said, only replace =180 with <180

say A, B, and C are the measures of the interior angles of the triangle.
Then A+B+C < 180
And the exterior angle of A, call it A', it measures 180-A

So...
180 - A > B + C

And the rest is history.

I'm sure you understood this, @Boblovesmath
It was just a tiny tweak in what you posted, right? ^_^

Answer 12

By supplementary angle axiom m<1 +m<2 = 180. By sum of triangles theorem <A + <B+m<2 <= 180.
So m<2 = 180-m<1.
<A+<B+180 -m<1 <= 180
thus <A + <B <= m<1. done.....(m<1 is my exterior angle)

Answer 13

A bit iffy, but correct in essence ^_^

Well done :)

Answer 14

thx for the help