Lesson 1: Angle Properties at a Point and on a Line

📘 Module 7: Plane Geometry – Part 1

Lesson 1: Angle Properties at a Point and on a Line

👨🏽‍🏫 Introduction

Have you ever stood at a crossroads and looked in all directions? Or noticed how the hands of a clock form a straight line at 6 o’clock? Those are real-life examples of angle properties in action!

This lesson introduces you to how angles behave around a point and along a straight line. These simple ideas are used everywhere — from designing roads and buildings to creating art and furniture. 🧱✏️

• 🧭 Understand angles around a point and on a straight line
• 🔄 Learn vertically opposite angles and why they’re always equal
• 📐 Apply rules to solve for unknown angles in geometry problems

🧠 Key Concepts

📌 1. Angles at a Point

All angles around a single point add up to:

All the angles created where these lines meet at the center add up to 360°.

📌 2. Angles on a Straight Line

Angles that lie next to each other on a straight line add up to:

x
y

Here, x and y are angles on a straight line and .

📌 3. Vertically Opposite Angles

When two lines cross, opposite (facing) angles are equal.

a
a
b
b

If one angle is , the one directly across from it is also — vertically opposite angles are always equal!

🔍 Worked Examples

1. 1. Example 1: One angle on a straight line is 130°. What is the other angle?

      
      
      🟢 The missing angle is 50°.

1. 1. Example 2: Three angles meet at a point: 90°, 110°, and x. Find x.

      Total =
      Known angles = 90 + 110 = 200
      
      🟢 So, x is 160°.

1. 1. Example 3: Two lines intersect. One angle is 72°. What is the vertically opposite angle?

      🟢 Vertically opposite angles are equal ⇒ Answer is also 72°.

1. Example 4: Three angles on a straight line are x, 2x, and 30°. Find x.

   
   
   🟢 The three angles are 50°, 100°, and 30°.

✍🏽 Practice Exercises

🅰️ Section A – Straight Line

1. If one angle is 135°, find the other angle on the straight line.
2. Find x if

🅱️ Section B – Angles at a Point

1. Angles around a point are 100°, 95°, and x. Find x.
2. Four angles meet at a point: 80°, 90°, 70°, and x. What is x?

🅾️ Section C – Vertically Opposite Angles

1. Two lines cross. One angle is 47°. What is the opposite angle?
2. If one opposite angle is x and the other is 3x, find x.

✅ Answers and Explanations

• A1:
• A2:
• B1:
• B2:
• C1: 47° (vertically opposite angles are equal)
• C2:

📌 Recap

• 🔄 Angles at a point add up to 360°
• ➗ Angles on a straight line add up to 180°
• 🎯 Vertically opposite angles are always equal

💭 Reflection Prompt

Have you ever seen corners, cross-roads, or clock hands form angles? Try sketching one and label the angles. Which angle rule helps you figure out a missing angle in your sketch?