A triangle can have a minimum of one acute angle.
To understand why, let’s first define what an acute angle is. An acute angle is an angle that measures less than 90 degrees. In any triangle, the sum of the internal angles always equals 180 degrees.
In a triangle with at least one acute angle, the other angles can be right angles or obtuse angles (which measure more than 90 degrees but less than 180 degrees). For example:
- A triangle with one acute angle and one right angle must have the last angle as an acute angle (since 90 degrees + acute angle leaves an acute angle to maintain the 180-degree total).
- A triangle with one acute angle and one obtuse angle must also have the last angle as an acute angle, as the obtuse angle would exceed the total allowable limit of 180 degrees.
Thus, while a triangle can have two or even three acute angles, it’s possible for a triangle to have just one acute angle and still satisfy the rules of triangle angles. Therefore, the least number of acute angles in a triangle is indeed one.