Lesson 2: Angles on Parallel Lines

👨🏽‍🏫 Introduction

Ever noticed how railway tracks run side by side and never meet, no matter how far they go? Those are parallel lines in real life. 🚆

Now imagine a ladder leaning across those tracks — the rungs of the ladder form angles with the tracks. These angles help us understand a special group of angle relationships created when a line crosses two parallel lines.

In this lesson, you’ll learn how to identify and calculate angles formed when a transversal cuts across parallel lines. This is useful in architecture, design, engineering, and solving many WASSCE questions! 🧠

• 📏 Understand parallel lines and transversals
• 🔁 Learn key angle relationships like corresponding, alternate, and co-interior angles
• 🎯 Apply rules to solve for unknown angles

🧠 Key Concepts

📌 1. Parallel Lines and a Transversal

Parallel lines are lines that never meet. A transversal is a line that cuts across them, forming angles:

This transversal creates angle pairs that follow specific rules when the two horizontal lines are parallel.

📐 2. Angle Relationships

✅ Corresponding Angles (F-shape)

If lines are parallel, then corresponding angles are equal:

a
a

Rule:

✅ Alternate Angles (Z-shape)

These angles lie inside the parallel lines but on opposite sides of the transversal:

b
b

Rule:

✅ Co-Interior Angles (C-shape)

These angles lie on the same side of the transversal and between the parallel lines:

c
d

Rule:

🔍 Worked Examples

1. 1. Example 1 – Corresponding Angles:
      If , find the angle corresponding to it on the other parallel line.

      🟢 The angle is also .

1. 1. Example 2 – Alternate Angles:
      One angle is . What is the alternate angle?

      🟢 Alternate angle = .

1. 1. Example 3 – Co-Interior Angles:
      If one co-interior angle is 112°, find the other.

      
      🟢 The other angle is 68°.

1. Example 4 – Mixed Angles:
   and it’s co-interior with a 100° angle. Find x.

   
   
   🟢 So, x = 55°.

✍🏽 Practice Exercises

🅰️ Section A – Corresponding Angles

1. If , find the corresponding angle.
2. Find the angle corresponding to .

🅱️ Section B – Alternate Angles

1. One alternate angle is 65°. What is the other?
2. Find x if is alternate to

🅾️ Section C – Co-interior Angles

1. If one angle is 105°, what is the co-interior angle?
2. Find x if the co-interior angles are and

✅ Answers and Explanations

• A1: 72° (corresponding)
• A2: 118° (corresponding)
• B1: 65° (alternate)
• B2: x = 80°
• C1:
• C2:

📌 Recap

• 📐 Corresponding angles are equal (F-shape)
• 🔁 Alternate angles are equal (Z-shape)
• ➕ Co-interior angles add up to (C-shape)

💭 Reflection Prompt

Look at a window grill, road markings, or staircase bars. Can you spot any angle relationships that match F, Z, or C shapes? Draw and label them based on what you’ve learned today!