Question

Karen says the angles of her triangle measure 90, 50, and 60. why is this impossible?

Answer 1

See below:

Explanation:

The inside angles of a triangle must always add up to 180 degrees.

There is no such thing as a triangle with angles adding to `179^@` or `181^@`. The three angles of a triangle must always add up to `180^@`.

`90 + 50 + 60 = 200`

`200 != 180`

Karen made some sort of error in her calculations, since the angles of her "triangle" are greater than `180^@`

Answer 2

This is impossible because the sum of a triangle's interior angles is 180°. The sum of the angles of Karen's triangle is 200, which exceeds 180°.

Explanation:

The Angle Sum Theorem of Triangles states that the angle measures in any form of triangle (scalene, right, isoceles, obtuse, acute) will add up to 180°.

This example from http://www.basic-mathematics.com/angle-sum-theorem.html shows the proof this way:

Angles a, c, and b make a straight line and are therefore, supplementary.

∠a + ∠c + ∠b = 180°

Because alternate interior angles are equal (when parallel at cut by a transversal), ∠a = ∠x and ∠b = ∠y

Therefore, when substituted, ∠x + ∠y + ∠c = 180°.

Credit to https://www.basic-mathematics.com/angle-sum-theorem.html for the examples and explanation.

For more info:
http://www.mathwarehouse.com/geometry/polygon/
https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-polygons/v/sum-of-interior-angles-of-a-polygon
http://mathopenref.com/triangleinternalangles.html