A Tale of Three Intersecting Lines - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Three intersecting lines can create a triangle, and the triangle becomes one of the most important shapes in mathematics. This chapter connects line-angle facts to triangle angle properties, helping students solve geometry problems without measuring every angle.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Triangle as three line segments

A triangle is formed by three line segments meeting pairwise. Its three interior angles have a fixed relationship.

Angle sum property

The angles inside any triangle add to 180 degrees. This holds for all triangles: acute, obtuse, right, scalene, isosceles, and equilateral.

Exterior angle

An exterior angle of a triangle equals the sum of the two opposite interior angles. This follows from the straight-line angle and angle-sum property.

3. Rules and formulas to remember

• Triangle angle sum: A + B + C = 180 degrees. For every triangle.
• Exterior angle property: Exterior angle = sum of two opposite interior angles. Useful for quick geometry.
• Equilateral triangle angle: 60 degrees each. All sides and all angles equal.
• Right triangle: Two acute angles sum to 90 degrees. Because the third angle is 90 degrees.

4. Worked examples

Example 1: A triangle has angles 45 degrees and 65 degrees. Find the third angle.

Third angle = 180 - (45 + 65) = 70 degrees.

Example 2: In a right triangle, one acute angle is 38 degrees. Find the other.

Other acute angle = 90 - 38 = 52 degrees.

Example 3: An exterior angle is 125 degrees and one opposite interior angle is 55 degrees. Find the other opposite angle.

Other opposite angle = 125 - 55 = 70 degrees.

Example 4: Can a triangle have angles 90, 60, and 40 degrees?

No. Their sum is 190 degrees, not 180 degrees.

5. Activity corner

Draw any triangle, tear off its three corners, and place the angle tips together on a straight line. They form 180 degrees, making the angle-sum property visible.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Assuming all triangle angles look equal Fix: Use angle facts, not the drawing's appearance.
• Mistake: Forgetting to add the two given angles before subtracting Fix: Third angle = 180 - sum of two angles.
• Mistake: Using exterior angle property with adjacent interior angle Fix: Use the two opposite interior angles only.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Find the third angle if two angles are 72 and 48 degrees.
2. Each angle of an equilateral triangle is?
3. A triangle has angles x, x, and 40 degrees. Find x.
4. Exterior angle is 110 degrees. One opposite angle is 35 degrees. Find the other.
5. Can angles 30, 70, 80 form a triangle?
6. Why do triangle problems often use 180 degrees?

9. Answer key

1. Find the third angle if two angles are 72 and 48 degrees. Answer: 60 degrees.

2. Each angle of an equilateral triangle is? Answer: 60 degrees.

3. A triangle has angles x, x, and 40 degrees. Find x. Answer: 70 degrees.

4. Exterior angle is 110 degrees. One opposite angle is 35 degrees. Find the other. Answer: 75 degrees.

5. Can angles 30, 70, 80 form a triangle? Answer: Yes, sum is 180 degrees.

6. Why do triangle problems often use 180 degrees? Answer: Because the interior angles of every triangle sum to 180 degrees.

10. Quick revision

• Main themes: triangles, angle sum, exterior angle, intersecting lines.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.