Q1. Two parallel lines are cut by a transversal. One angle is 70°. Find the co-interior angle.
Co-interior angles are supplementary (sum to 180°)
180° − 70° = 110°
The co-interior angle is 110°.
Lines and Angles — Class 9
Two lines crossing create a whole family of equal and supplementary angles — learn the rules once and use them forever.
Linear pairTwo adjacent angles on a straight line; they add up to 180° (supplementary).
Vertically opposite anglesFormed by two intersecting lines; they are always equal.
Transversal angle pairsA line cutting two parallel lines creates corresponding angles (equal), alternate interior angles (equal), and co-interior angles (supplementary, sum 180°).
Solved examples
Q2. In a triangle, two angles are 50° and 60°. Find the third and the exterior angle at that vertex.
Angle sum of a triangle = 180°
Third angle = 180° − 50° − 60° = 70°
Exterior angle = 180° − 70° = 110° (= 50° + 60°, matching the exterior-angle rule)
Formula sheet
| Quantity | Formula |
|---|---|
| Linear pair | sum = 180° |
| Angle sum of a triangle | sum = 180° |
| Exterior angle of a triangle | = sum of the two interior opposite angles |
Common mistakes & exam wins
- Corresponding angles are equal; alternate interior angles are equal; co-interior angles sum to 180° — but ONLY when the lines are parallel.
- Vertically opposite angles are always equal, whether or not the lines are parallel.
- The exterior angle of a triangle equals the sum of the two non-adjacent interior angles — a quick shortcut.
Frequently asked questions
What is a linear pair of angles?
Two adjacent angles whose non-common arms form a straight line; they always sum to 180°.
Are vertically opposite angles always equal?
Yes, whenever two lines intersect, the pairs of vertically opposite angles formed are always equal.
What is the sum of the angles of a triangle?
180°, always — this is the angle sum property of a triangle.