Acute-angled triangles
All the angles in an acute-angled triangle are smaller than 90°.
Right-angled triangles
The name sort of says it all – right-angled triangles have a right angle in them. It’s important to remember that since there is only a total of 180° in the interior angles of a triangle, you can’t have more than one right angle inside a triangle. If you had two right angles, the third angle would have to be zero degrees, and there’s no way you can draw a triangle with one of the angles being zero.
Now because one of the angles in the triangle is a right angle, the other two angles must add up to 90 degrees:
This means that ‘a’ and ‘b’ must each be smaller than 90°. So the other two angles in a right-angled triangle are acute angles.
Obtuse-angled triangles
Obtuse-angled triangles have one angle in them which is larger than 90°.
This means that the other two angles in the triangle must together add up to something less than 90 degrees. So obtuse-angled triangles have one obtuse angle and two acute angles in them.