📚 What is a Linear Pair of Angles?
A linear pair of angles is a set of two angles that share a common side and vertex, and their non-common sides form a straight line. The sum of the measures of a linear pair of angles is always 180 degrees. They are supplementary!
📐 Key Properties of Linear Pairs
- 🤝 Adjacent Angles:
🔍 Linear pairs are always adjacent, meaning they share a common vertex and a common side.
- 📏 Supplementary Angles:
💡 The sum of the measures of the two angles in a linear pair is always 180 degrees. If one angle is $x$ and the other is $y$, then $x + y = 180^{\circ}$.
- ➖ Forms a Straight Line:
📝 The non-common sides of the angles in a linear pair form a straight line.
✍️ Examples of Linear Pairs
Imagine a straight line. Now, pick a point on that line and draw another line from that point, creating two angles. Those two angles form a linear pair.
- ➕ Example 1:
➗ If one angle in a linear pair measures 60 degrees, the other angle measures 120 degrees because $60^{\circ} + 120^{\circ} = 180^{\circ}$.
- ➖ Example 2:
📈 If one angle is a right angle (90 degrees), the other angle must also be a right angle because $90^{\circ} + 90^{\circ} = 180^{\circ}$.
🧮 How to Identify Linear Pairs
- 👀 Visual Inspection:
👓 Look for two angles that share a vertex and a side, forming a straight line.
- ➕ Check for Supplementarity:
🔢 Verify that the sum of the measures of the two angles is 180 degrees.
📝 Practice Quiz
Determine if the following angle pairs are linear pairs. Provide a brief justification.
- Angles measuring 70° and 110°
- Angles measuring 90° and 90°
- Angles measuring 60° and 130°
- Angles measuring 45° and 135°
- Angles measuring 100° and 80°
- Angles measuring 30° and 150°
- Angles measuring 20° and 160°
✅ Solutions to Practice Quiz
- No, 70° + 110° = 180°. They are supplementary, but must be adjacent to be a linear pair.
- Yes, 90° + 90° = 180°. If they share a side, they are a linear pair.
- No, 60° + 130° = 190°. They do not add up to 180 degrees.
- Yes, 45° + 135° = 180°. If they share a side, they are a linear pair.
- Yes, 100° + 80° = 180°. If they share a side, they are a linear pair.
- Yes, 30° + 150° = 180°. If they share a side, they are a linear pair.
- Yes, 20° + 160° = 180°. If they share a side, they are a linear pair.