Why is it impossible to create a triangle with two angles greater than 60 degrees?

Answer 1

The only facts involving the angles in a triangle are
1: Angles are all positive
2: Sum of the angles is 180 degrees

This means I can have a triangle with two angles of 89.5 degrees and the remaining one of 1 degree.

Yes; it would be hard to draw but it can be done.

So no, it is NOT impossible to create a triangle with two angles greater than 60 degrees.

However, you can not have a triangle with two angles greater than 90.

Let a and b be >= 90

We know a + b + c = 180
But since a and b are both >= 90, then (a+b) >= 180
so c <= 0
which is impossible (since all angles in a triangle are > 0).

Answer 2

It isn't impossible. It IS impossible to create a triangle with two angles of 90 degrees or more. That is because the angles in a triangle add up to 180 degrees and there must be three of 'em. Two 90 degree angles leave nothing for the third.

Answer 3

It is possible to create a triangle with two angles greater than 60 degrees. Say for example, 70, 70, 40. Sum all the angles it totals 180 degrees but it is impossible to create a triangle with two angles equal to 90 degrees

Answer 4

If the triangle is in a flat Euclidean plane then the sum of the interior angles of a triangle is 180 degrees. This the defining criteria. Two of the angles can be as large as you like so long as their sum is < 180 degrees.

Note that the triangle must be in a flat plane. If it is in a curved plane (non Eucldean geometry) then it is not true. Imagine two people on the equator and the line between them forms the base of a triangle. They both walk towards the North pole. The line that both people walk is at 90 dgrees to the base of the triangle. However, they will both meet at the North pole where the sides of the traingle will meet and there will be an angle between these lines at the North pole. Its size depends on how far apart the people were on the equator. In this case the sum of the angles of the triangle will be > 180 degrees.

Answer 5

It's possible. The internal angles of a triangle add up to 180 degrees. Two of those angles can increase up to 90, but not equal 90 or more. Is that what you meant?

Answer 6

It is possible. Take an isosceles triangle with
base angles 75 degrees. The remaining angle
is 30 degrees.

Answer 7

Sum all the angles it totals 180 degrees and each angles less than 90 degrees.

hug.

Answer 8

PETER, can we say contradiction :
you say "This means I can have a triangle with two angles of 89.5 degrees and the remaining one of 1 degree.

Yes; it would be hard to draw but it can be done.
THEN YOU SAY:::

So no, it is NOT impossible to create a triangle with two angles greater than 60 degrees.

so which is it?

Answer 9

because with any two angles under 90 degrees, the lines will always meet each other as they slant inwards
(towards each other). the lines may have to be pretty long though, depending on the size of the base.
however, with two angles of 90 or above the lines are perpendicular or slant away from each other, so they will never meet.

does this help???

Answer 10

philly is wrong

It is possible as long as the two angle add up to less than 180◦

you could have a base with two angles that are both 89.9999◦ and you would still be able to produce a triangle