Lines & Angles

🎯 Learning Objective

Use complementary, supplementary and parallel-line angle rules to find unknown angles instantly.

💡 Concept

• Complementary angles add to 90°; supplementary angles add to 180°
• Vertically opposite angles are always equal
• Angles on a straight line (linear pair) add to 180°
• Parallel lines + transversal: corresponding and alternate angles are EQUAL
• Co-interior (same-side interior) angles add to 180°

🧮 Key Formulas

Complementary: A + B = 90°

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Supplementary: A + B = 180°

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Co-interior angles = 180°

✏️ Easy Example

Q. Find the complement of 35°.

1. Complement = 90° − 35°

Answer: 55°

🇮🇳 Real-Life Example

Railway tracks are parallel lines and the road crossing them is a transversal — every angle at that crossing follows these exact rules.

📝 Exam-Level Example

Q. Two supplementary angles are in the ratio 2 : 3. Find the angles.

1. 2x + 3x = 180
2. 5x = 180 → x = 36
3. Angles: 2×36 and 3×36

Answer: 72° and 108°

📝 Exam-Level Example

Q. Two parallel lines are cut by a transversal. One co-interior angle is 65°. Find the other.

1. Co-interior pair sums to 180°
2. 180 − 65 = 115

Answer: 115°

🪄 Memory Trick

In any parallel-line figure, two marked angles are either EQUAL or SUPPLEMENTARY. Both acute or both obtuse → equal; one acute one obtuse → 180°.

⚠️ Common Mistakes

• ❌ Mixing up complementary (90°) with supplementary (180°)
• ❌ Treating co-interior angles as equal — they add to 180°

🏆 Exam Tips

• ✅ Memory hook: C comes before S, 90 comes before 180
• ✅ No figure given? Draw one — half the answer appears on paper

📌 Summary

• Complementary 90°, supplementary 180°
• Vertically opposite → equal
• Parallel + transversal: corresponding/alternate equal, co-interior 180°