All triangles have at least 2 acute angles?

Answer 1

True. The reasoning behind it is this: the sum of the angles in any triangle will always equal 180o.

Equilateral (all sides & angles equal)

3x = 180

x = 60

Isosceles (two equal sides & angles) - can include Right triangle (90 + 45 + 45)

x + 2y = 180

y = (180-x)/2

No matter what x equals (acute, right, or obtuse), y will be less than 90 (acute) because half of 180 is 90 and half of anything less than 180 will be less than 90.

Scalene (all sides & angles different) - can include Right triangle (90 + x + y)

x + y + z = 180

If one angle is obtuse...

x > 90

180 - x < 90

y + z < 90

If together they are less than 90, then clearly both are less than 90 (acute)