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

See below:

Triangles always have interior angles that add up to 180 degrees.

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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°.

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 https://tutor.hix.ai 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://tutor.hix.ai for the examples and explanation.

For more info:

https://tutor.hix.ai
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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