What are Supplementary Angles? 7th Grade Math Guide

📚 What are Supplementary Angles?

In geometry, supplementary angles are two angles whose measures add up to $180$ degrees. Think of it as half a circle or a straight line. When you combine the measures of these two angles, you always get $180^{\circ}$.

📜 A Bit of History

The study of angles and their relationships dates back to ancient civilizations like the Egyptians and Babylonians. These early mathematicians needed to understand angles for construction, navigation, and astronomy. The concept of supplementary angles, while not explicitly named as such, was crucial in their geometric calculations and designs. The formal definitions and theorems we use today were later developed by the Greeks, particularly Euclid, whose work "Elements" laid the foundation for much of modern geometry.

📐 Key Principles of Supplementary Angles

• ➕ Definition: 2 angles are called supplementary if their sum is $180^{\circ}$.
• 📏 Straight Line: Supplementary angles often form a straight line when placed adjacent to each other.
• 🧮 Calculation: If you know the measure of one angle, you can find the measure of its supplement by subtracting it from $180^{\circ}$.
• 🤝 Pairing: Supplementary angles always come in pairs.

🌍 Real-World Examples

Supplementary angles are all around us! Here are some examples:

• ✂️ Scissors: When you open a pair of scissors, the two angles formed at the joint are often supplementary.
• 🛤️ Railroad Tracks: The angles formed where a diagonal support beam intersects a straight railroad track are sometimes supplementary.
• 🛹 Skateboard Ramp: The angle of the ramp and its adjacent angle on the flat ground can be supplementary.
• 📐 Roof Truss: The supporting structures of roofs frequently use supplementary angles to distribute weight.

📝 Finding Supplementary Angles

Let's say you have an angle that measures $60^{\circ}$. To find its supplementary angle, you simply subtract $60^{\circ}$ from $180^{\circ}$:

$180^{\circ} - 60^{\circ} = 120^{\circ}$

So, the supplementary angle is $120^{\circ}$.

❓ Practice Quiz

Determine the supplementary angle for each given angle:

1. If an angle is $30^{\circ}$, its supplementary angle is: $180^{\circ} - 30^{\circ} = 150^{\circ}$
2. If an angle is $90^{\circ}$, its supplementary angle is: $180^{\circ} - 90^{\circ} = 90^{\circ}$
3. If an angle is $45^{\circ}$, its supplementary angle is: $180^{\circ} - 45^{\circ} = 135^{\circ}$
4. If an angle is $120^{\circ}$, its supplementary angle is: $180^{\circ} - 120^{\circ} = 60^{\circ}$
5. If an angle is $15^{\circ}$, its supplementary angle is: $180^{\circ} - 15^{\circ} = 165^{\circ}$
6. If an angle is $75^{\circ}$, its supplementary angle is: $180^{\circ} - 75^{\circ} = 105^{\circ}$
7. If an angle is $135^{\circ}$, its supplementary angle is: $180^{\circ} - 135^{\circ} = 45^{\circ}$

⭐ Conclusion

Understanding supplementary angles is a fundamental concept in geometry. Once you grasp the idea that they add up to $180^{\circ}$, you'll see them everywhere! Keep practicing, and you'll become a master of angles in no time!