What is the greatest number of right angles that a triangle can contain?

1 Answer
May 1, 2016

One.

Explanation:

A triangle has #180^o# as the sum of all its internal angles, no more, no less.

If one angle is #90^o#, then you can have two #45^o# angles, one #30^o# and a #60^o#, an #81^o# and a #9^o# - pretty much any combination of numbers adding up to #90# to make the total #90+90=180#.

If two angles are #90^o#, this makes #90+90=180# as the sum of internal angles straight off the bat, so the last angle must be #0^o# to keep the total sum of internal angles at #180^o#. But an angle of #0# doesn't really exist - it's just a straight line - so a triangle can't have two or more right angles.

The most possible right angles in any triangle therefore must be one.