SOLUTION: Which one of the following could represent two of the three angles of an acute triangle? 28 degrees and 66 degrees 4 degrees and 100 degrees 60 degrees and 10 degrees 31 degree

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°  

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.

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.

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.

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