Any angle less than 90° is an acute angle.
Every triangle has two acute angles.
But some triangles have all three angles acute.
When all three angles of a triangle are acute, we call
it an "acute triangle".
Since we know that the sum of the three angles of
every triangle is 180°, then if we know two angles, we
can find the third angle by adding those two and subtracting
from 180°
28 degrees and 66 degrees
Those two angles are acute because they are both less than 90°.
We add them 28° + 66° and get 94°.
Now we subtract 180° - 94° and get 86°.
So therefore all thre angles of that triangle are less than
90°, so we know that it IS an ACUTE triangle.
4 degrees and 100 degrees
We know immediately that this is not an acute triangle because
100° is NOT an acute angle, because it is greater than 90°.
Angles greater than 90° are called "obtuse", and so this is
NOT an acute triangle. It is an obtuse triangle.
60 degrees and 10 degrees
Those two angles are acute because they are both less than 90°.
We add them 60° + 10° and get 70°.
Now we subtract 180° - 70° and get 110°.
But 110° is greater than 90°, therefore this is NOT an
acute triangle. It's an obtuse triangle.
31 degrees 59 degrees
Those two angles are acute because they are both less than 90°.
We add them 31° + 59° and get 90°.
Now we subtract 180° - 90° and get 90°.
But 90° is NOT greater than 90°, therefore this is NOT an
acute triangle. It's a RIGHT triangle, because it has a
90° angle.
Edwin