# How many acute angles can a scalene triangle have?

Nov 23, 2015

A scalene triangle can have either $2$ or $3$ acute angles.

#### Explanation:

A scalene triangle is any triangle with no repeated angle measures.

There are three general ones:

1. An acute scalene triangle, where all $3$ of the angles are less than 90˚. An example would be a triangle with degree measures 30˚, 70˚, and 80˚. All three of its angles have different measures and are all acute. (3 acute angles)

2. A right scalene triangle. Any right triangle will have one degree whose measure is 90˚, and the other two angles must be acute. An example would be the very common 30˚-60˚-90˚ triangle, which, again, has two acute angles. (2 acute angles)

3. An obtuse scalene triangle. This is very similar to the right scalene triangle, except it has one angle whose measure is greater than 90˚, and two acute angles. (2 acute angles)