Very Obtuse

Geometry Level 2

What is the largest measure that an internal angle in a triangle might have?

90^\circ

180^\circ

360^\circ

There is no maximum magnitude for the internal angle of a triangle.

2 solutions

Zandra Vinegar Staff
Jan 23, 2016

There is no maximum magnitude for the internal angle of a triangle because, while such angles can be very nearly $180^\circ$ , they cannot actually be $180^\circ$ . Therefore, no real-number value can be the "maximum."

If one were to try to claim that some specific number less than $180^\circ$ was the maximum, I would simply respond that one slightly closer to $180^\circ$ is actually a bit larger, disproving the initial claim.

Saying that a triangle with zero area turns into a line is absurd, why would the two short sides disappear because they are eclipsed by a longer line?

This section is patently false and a dangerous spread of misinformation from people with problems to grasp abstract math.

Look up the triangle inequality again and compare it to the version used for the proof in the official "answer". For such a simple theorem this is a grave error

Marcus Appelros - 3 years, 7 months ago

The number tends towards 180° but is smaller than 180°.

Sören Fischötter - 3 years, 5 months ago

kind of reminds me of the absolute min or max on a segment of a curve with open intervals

A Former Brilliant Member - 2 years, 9 months ago

. .
Apr 24, 2021

The sum of three angles of a triangle is equal to 180 degrees, so if the triangle is equilateral, then, two angles are 0.00000000......1 degrees, and the other angle is 179.99999.....8 degrees.

But we cannot measure it exactly, so no maximum exists.

this is a great answer and it is correct

Aaren Ruparel - 3 weeks, 1 day ago

Very Obtuse

2 solutions

0 pending reports