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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 1 exam through angle calculations and constructions

Geometry (Term 1) - Lines and Angles

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 1 Chapter 5, Geometry. Points, lines, rays and line segments, types of angles, pairs of angles (complementary, supplementary, linear pair, adjacent and vertically opposite), parallel lines cut by a transversal, and the construction of special angles and the perpendicular bisector, with worked examples, exercises and quick revision.

⏱ 15 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Distinguish points, lines, rays and segments
2Classify angles by their measure
3Use complementary, supplementary and linear-pair relationships
4Apply parallel-line and transversal angle rules
5Construct special angles and the perpendicular bisector

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Why this chapter matters

Lines and angles are the language of all geometry. Angle pairs, parallel-line relationships and basic constructions are directly tested in the TN Class 7 Term 1 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 6 — Basic Geometrical Ideas

Points, lines and angles.

Geometry (Lines and Angles) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 1 — Chapter 5. Lines, angles and the relationships between them.

1. About this chapter

This chapter covers points, lines, rays and line segments, types of angles, pairs of angles, parallel lines and transversals, and the construction of special angles and the perpendicular bisector.

2. Basic terms

A point marks a position; a line extends endlessly both ways; a ray has one endpoint and extends one way; a line segment has two endpoints.
Intersecting lines cross at a point; parallel lines never meet.

3. Types of angles

Type	Measure
Acute	between 0° and 90°
Right	exactly 90°
Obtuse	between 90° and 180°
Straight	exactly 180°
Reflex	between 180° and 360°

4. Pairs of angles

Complementary angles: add up to 90°.
Supplementary angles: add up to 180°.
Linear pair: two adjacent angles on a straight line that add up to 180°.
Vertically opposite angles (formed when two lines cross) are equal.
Adjacent angles share a common vertex and arm.

5. Parallel lines and a transversal

When a transversal cuts two parallel lines:

corresponding angles are equal,
alternate angles are equal, and
co-interior (same-side) angles are supplementary (add to 180°).

6. Worked examples

Example 1. The complement of 35° is ____. 90° − 35° = 55°.

Example 2. Two angles of a linear pair: one is 110°. Find the other. 180° − 110° = 70°.

Example 3. Two lines cross; one angle is 65°. Find the vertically opposite angle. Vertically opposite angles are equal → 65°.

7. Exercises (Samacheer Kalvi)

Find the complement of (a) 40° (b) 72°.
Find the supplement of (a) 95° (b) 130°.
Two angles form a linear pair; one is 48°. Find the other.
Construct an angle of 60° using a compass.
Draw the perpendicular bisector of a line segment of length 7 cm.

8. Common mistakes

Mistake: Swapping complementary and supplementary. Fix: Complementary = 90°; supplementary = 180°.
Mistake: Thinking vertically opposite angles are supplementary. Fix: Vertically opposite angles are equal.
Mistake: Confusing a line, ray and segment. Fix: A line has no endpoints, a ray one, a segment two.

9. Quick revision

Term 1 · Ch 5 · lines and angles.
Point/line/ray/segment; acute < 90° < obtuse < 180° (straight) < reflex.
Complementary add to 90°; supplementary and linear pair add to 180°; vertically opposite are equal.
Transversal on parallel lines: corresponding and alternate angles equal; co-interior supplementary.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Complementary

two angles add to 90°

Complement = 90° − angle.

Supplementary / linear pair

two angles add to 180°

Supplement = 180° − angle.

Vertically opposite

equal angles when two lines cross

Always equal.

Transversal on parallels

corresponding & alternate equal; co-interior supplementary

Parallel-line rules.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Swapping complementary and supplementary

✓ Complementary = 90°; supplementary = 180°.

WATCH OUT

✗ Thinking vertically opposite angles are supplementary

✓ Vertically opposite angles are equal.

WATCH OUT

✗ Confusing a line, ray and segment

✓ A line has no endpoints, a ray one, a segment two.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Complement and supplement

Find complements and supplements of angles.

Questions

Angle pairs

Linear pair and vertically opposite angles.

Questions

Constructions

Special angles and perpendicular bisector.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Complement

Find the complement of 40°.

▶ Show solution

90° − 40° = 50°.

Q2EASY· Supplement

Find the supplement of 130°.

▶ Show solution

180° − 130° = 50°.

Q3EASY· Linear pair

Two angles form a linear pair; one is 48°. Find the other.

▶ Show solution

180° − 48° = 132°.

Q4MEDIUM· Vertically opposite

Two lines cross; one angle is 65°. Find all four angles.

▶ Show solution

65°, 115°, 65°, 115° (vertically opposite equal; linear pairs supplementary).

Q5MEDIUM· Construction

How do you construct a 60° angle with a compass?

▶ Show solution

Draw a ray, mark an arc from the vertex, then from where it cuts the ray mark another arc of the same radius; join the vertex to the intersection.

Q6EASY· Classify

What type of angle is 135°?

▶ Show solution

Obtuse (between 90° and 180°).

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 1 Chapter 5 of Samacheer Kalvi Class 7 Maths.
•Point, line, ray and segment differ by their endpoints.
•Angles: acute < 90°, right = 90°, obtuse < 180°, straight = 180°, reflex < 360°.
•Complementary add to 90°; supplementary and linear pairs add to 180°.
•Vertically opposite angles are equal.
•On parallel lines cut by a transversal: corresponding and alternate angles equal, co-interior supplementary.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across angle work and constructions

Question type	Marks each	Typical count	What it tests
Objective	1	3-5	Complement, supplement, angle type
Angle pairs	2	1-2	Linear pair, vertically opposite
Construction	2	1	Special angle or perpendicular bisector

Prep strategy

Memorise 90° and 180° for the angle pairs
Use vertically opposite = equal
Practise compass constructions
Learn the parallel-line angle rules

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Construction

Builders use angle rules to make accurate corners.

Design

Roads, ramps and patterns rely on angle measurement.

Navigation

Directions and bearings use angles.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Quote 90° / 180° for the angle pairs
Mark equal vertically opposite angles
Show construction arcs clearly
Use parallel-line rules to find unknown angles

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Two parallel lines are cut by a transversal; one co-interior angle is 3x and the other 2x. Find x.
Construct a 75° angle using compass and ruler only.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 7 Term 1 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Complementary angles add up to 90°, while supplementary angles add up to 180°.

When two lines cross, each pair of vertically opposite angles is supplementary to the same adjacent angle, so the two opposite angles must be equal.

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