Supplementary Angles Explained: Properties and Examples

📚 Quick Study Guide

• 📐 Two angles are supplementary if their measures add up to $180^\circ$.
• ➕ If $\angle A$ and $\angle B$ are supplementary, then $m\angle A + m\angle B = 180^\circ$.
• 💡 Supplementary angles can be adjacent (sharing a common vertex and side) or non-adjacent.
• 🧭 A linear pair of angles are always supplementary.
• ✍️ To find the supplement of an angle, subtract its measure from $180^\circ$.

✍️ Practice Quiz

1. What is the supplement of a $60^\circ$ angle?
   1. $30^\circ$
   2. $90^\circ$
   3. $120^\circ$
   4. $240^\circ$
2. If $\angle X$ and $\angle Y$ are supplementary and $m\angle X = 110^\circ$, what is $m\angle Y$?
   1. $30^\circ$
   2. $70^\circ$
   3. $90^\circ$
   4. $20^\circ$
3. Which pair of angles are supplementary?
   1. $45^\circ$ and $45^\circ$
   2. $30^\circ$ and $60^\circ$
   3. $90^\circ$ and $100^\circ$
   4. $80^\circ$ and $100^\circ$
4. Two angles form a linear pair. If one angle measures $55^\circ$, what is the measure of the other angle?
   1. $35^\circ$
   2. $45^\circ$
   3. $125^\circ$
   4. $135^\circ$
5. $\angle P$ and $\angle Q$ are supplementary. If $m\angle P = 2x$ and $m\angle Q = 3x$, what is the value of $x$?
   1. $30$
   2. $36$
   3. $40$
   4. $45$
6. Which of the following statements is always true for supplementary angles?
   1. They are adjacent.
   2. They are congruent.
   3. Their measures add up to $90^\circ$.
   4. Their measures add up to $180^\circ$.
7. If the measure of an angle is $x$, what is the measure of its supplement?
   1. $90 - x$
   2. $x - 90$
   3. $180 - x$
   4. $x - 180$