Lines and Angles: Class 9 Study Guide
Angles that meet on a line, at a point or between parallel lines follow clear rules.
A pair of angles is complementary if they add up to 90° and supplementary if they add up to 180°. Two angles that share a vertex and an arm, and lie on a straight line, form a linear pair, so they add up to 180°. When two lines cross, vertically opposite angles are equal.
When a line, called a transversal, crosses two parallel lines, the angles it makes follow rules too.
Parallel lines and a transversal
| Angle pair | Rule when the lines are parallel |
|---|---|
| Corresponding angles | Equal |
| Alternate interior angles | Equal |
| Co-interior (same side) angles | Add up to 180° |
Angle sum of a triangle
The three angles of a triangle add up to 180°. The exterior angle of a triangle equals the sum of the two interior opposite angles. In a triangle with angles 50° and 60°, the third angle is 180° − 110° = 70°, and the exterior angle at the 70° corner is 110°.
Write them on the figure.
Linear pair, parallel or triangle?
Using the rule.
Do the angles add up?
An unknown angle
Two parallel lines are cut by a transversal. One angle is 65°. Its corresponding angle is also 65°, and the co-interior angle is 180° − 65° = 115°. A common exam method is to write the reason beside each step, for example: 'corresponding angles, parallel lines'.
Worked examples and common mistakes
Example: Two angles of a linear pair are x and 2x. Then 3x = 180, so x = 60°, and the angles are 60° and 120°. Example: The complement of 35° is 55°. Common mistakes: using the parallel-line rules when the lines are not parallel, and mixing up complementary (90°) and supplementary (180°). Remember: C comes before S, 90 comes before 180.
Check your understanding: model answers
1. 68°. 2. 180° − 125° = 55°. 3. 180° − 72° = 108°.
✨ Key Takeaways
- Complementary angles add to 90° and supplementary angles to 180°.
- Vertically opposite angles are equal.
- Parallel lines give equal corresponding and alternate angles.
- A triangle's angles add to 180°.
💬 Questions for Discussion & Reflection
- Find the supplement of 112°.
- Two angles of a triangle are 48° and 77°. Find the third.
- The corresponding angle is 72°. What is the co-interior angle?