Complementary angles are a fundamental concept in geometry. They are two angles whose measures add up to 90 degrees. This relationship is easy to remember if you think of the word ‘complementary’ as completing a right angle.
Key Properties of Complementary Angles
Sum of Angles
The defining property of complementary angles is that their measures add up to 90 degrees. For instance, if one angle measures 30 degrees, the other must measure 60 degrees to be complementary. Mathematically, if angle $A$ and angle $B$ are complementary, then:
$A + B = 90^text{°}$
Real-Life Examples
Complementary angles appear in various real-life situations. For example, when you open a book, the angle between the pages and the table can form complementary angles. If one page forms a 30-degree angle with the table, the other page forms a 60-degree angle.
Non-Adjacent Complementary Angles
It’s important to note that complementary angles do not have to be adjacent (next to each other) or form a right angle themselves. They only need to add up to 90 degrees. For example, one angle could be in one part of a diagram, and its complement could be somewhere else entirely.
Examples and Practice
Example 1
If you have one angle that measures 45 degrees, its complementary angle would be:
$90^text{°} – 45^text{°} = 45^text{°}$
So, both angles are 45 degrees.
Example 2
If one angle is 25 degrees, the complementary angle would be:
$90^text{°} – 25^text{°} = 65^text{°}$
Practice Problem
Find the complementary angle of a 70-degree angle. Using the formula:
$90^text{°} – 70^text{°} = 20^text{°}$
So, the complementary angle is 20 degrees.
Conclusion
Understanding complementary angles is essential for solving various geometric problems and can be quite practical in real-world scenarios. Knowing that two angles add up to 90 degrees can help you quickly identify missing angle measures and understand more complex geometric relationships.
3. CK-12 Foundation – Complementary Angles