Example 1:The sum of the angles in a triangle is 180º. Hence any triangle should contain at least two acute angles.
When all the three angles of the triangle are acute, the triangle is classified as an acute angled triangle.
Example 2:If an angle is acute, then its complementary is also acute, but is supplementary is obtuse.
For example, consider the angle measure 50º. Its complementary = 90 50 = 40 < 90 and hence acuted.
The supplementary of 50 is 180  50 = 130 > 90, which is obtuse.
Example 3:
A parallelogram whose adjacent sides are not perpendicular has one pair of acute angles equal measure and placed opposite to each other. 

Example 4:
When a Pizza is cut into eight pieces as shown, each of the angles 1 to 8 formed at the center are acute angles. 

Solved Example
Question: In the adjoining diagram QT is perpendicular to PR. Identify the acute angles so formed.
Solution:
Angles PQT and RQT are right angles
Hence, ∠PQU, ∠UQT, ∠TQS and ∠SQR are all acute angles.
We cannot classify ∠UQS as we do not know the measures of angles UQT and TQS.