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REET L1+L2 · Maths

Lines and Angles

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In REET Maths, Lines and Angles questions aren't based on straight definitions — they need you to set up and solve an equation. Here are all the rules for complementary-supplementary angles, linear pairs, vertically opposite angles, and parallel lines cut by a transversal, with worked examples.

  • 4 questions in REET 2024
  • Class 7 level
  • 9 min read
Verified 17 September 2026

How REET asks this topic

In all four of REET 2024's questions, a relationship between angles was given (a ratio of complementary-supplementary angles, the sum of several angles on one line, or angles formed at parallel lines), and it had to be turned into an equation in one variable, 'x'. The biggest thing to watch for: after solving the equation for 'x', you must substitute it back into the expression for the angle the question actually asks about (say, ∠AOD) — the value of x alone is not the final answer.

Types of angles, by measure

An angle between 0° and 90° is called an acute angle, an angle of exactly 90° is a right angle, and an angle between 90° and 180° is an obtuse angle. An angle of exactly 180° is called a straight angle, and an angle between 180° and 360° is a reflex angle. An angle of exactly 360° is a complete angle.

REET often gives the measure of an angle in a figure and asks you to name its type, so these six boundaries (0°, 90°, 180°, 360°) should be second nature.

Basic angle pairs

Two angles whose sum is 90° are called complementary angles. Two angles whose sum is 180° are called supplementary angles.

Two angles that share a vertex and a common arm, without overlapping each other, are called adjacent angles. When the non-common arms of two adjacent angles together form a straight line, they're called a linear pair, and the angles of a linear pair always add up to 180°.

When two straight lines intersect, the angles formed directly opposite each other are called vertically opposite angles, and these are always equal.

Angles formed by a transversal cutting parallel lines

Angle pairRelationship (when the lines are parallel)
Corresponding anglesEqual
Alternate interior anglesEqual
Alternate exterior anglesEqual
Co-interior / consecutive interior anglesSum is 180° (supplementary)

These four rules apply only when the two lines being cut by the transversal are actually parallel to each other.

Essential rules on angle sums

Sum of all angles formed on one side of a line
180°
Sum of all angles formed around a point
360°
Both angles of a linear pair
Always supplementary (sum 180°)
Vertically opposite angles
Always equal

How to solve by forming an equation

When a question gives a ratio or difference between an angle and its complement/supplement, take the angle as x and set up an equation. Example: if the supplement of an angle is three times its complement, find the angle.

Solution: let the angle = x. Complement = 90° − x, supplement = 180° − x. By the given condition, 180 − x = 3(90 − x) ⇒ 180 − x = 270 − 3x ⇒ 2x = 90 ⇒ x = 45°. Setting up and solving an equation like this is the core skill for this topic.

Another example, involving parallel lines: two parallel lines are cut by a transversal, forming an angle of (2x + 15)°, whose co-interior angle is (3x − 5)°. Find x and both angles. Solution: co-interior angles sum to 180°, so (2x + 15) + (3x − 5) = 180 ⇒ 5x + 10 = 180 ⇒ 5x = 170 ⇒ x = 34. First angle = 2(34) + 15 = 83°, second angle = 3(34) − 5 = 97°; check: 83° + 97° = 180°, correct.

How to teach children

Classroom activity

Join two straight strips (like rulers or ice-cream sticks) at the centre with a pin and rotate them, then measure the vertically opposite and linear-pair angles formed with a protractor and compare. Students can be grouped to form different angles and cross-check each other's measurements.

Teaching aids

A protractor, a geometry box, forming angles by paper folding — this makes complementary-supplementary angles visually clear. Placing a third rod across two parallel rods can also demonstrate all eight angles formed by a transversal.

Common misconception

Students often mix up 'complementary' (90°) and 'supplementary' (180°) because the words sound alike. Some children assume every pair of adjacent angles is a linear pair, when a linear pair specifically needs the arms to form a straight line; and some assume corresponding/alternate angles are equal without first checking that the lines are parallel.

Assessment idea

Show a real photo (like open scissors, a ladder against a wall, railway tracks) and ask students to identify the angles formed and name their type (complementary/supplementary/linear pair/corresponding), and explain their reasoning.

Memory trick / exam tip

The biggest mistake in Lines and Angles questions is finding the value of x and stopping there. After solving the equation for x, substitute it back into the expression for the angle actually being asked about (like ∠AOD = 5x) to get the real answer. Also, always verify whether a given angle pair really is a linear pair or just adjacent angles — not every adjacent pair is supplementary.

Questions asked in REET 2024 (with solutions)

Question 104

If an angle is twice its complementary angle, then the value of that angle will be

  1. A35°
  2. B45°
  3. C60°
  4. D90°

Explanation

मान लें कोण = x, तो उसका पूरक कोण = 90° − x। शर्त: x = 2(90° − x) ⇒ 3x = 180° ⇒ x = 60°। जाँच: 60° का पूरक 30° है और 60° = 2 × 30°।

Question 112

In the given figure, the value of ∠AOD is

Figure: DOC is a straight line with O on it. Rays OA and OB rise from O into the upper half. Angle AOD is (5x) degrees, angle BOA is (3x-2) degrees, and angle COB is (x+2) degrees. Diagram added and verified: solving gives x=20, so angle AOD = 100 degrees, matching the stored answer.

  1. A60°
  2. B90°
  3. C100°
  4. D20°

Explanation

DOC एक सरल रेखा है, अतः उस पर बने सभी कोणों का योग 180° होगा: 5x + (3x − 2) + (x + 2) = 180° ⇒ 9x = 180° ⇒ x = 20°। इसलिए ∠AOD = 5x = 100°। विकल्प (D) 20° केवल x का मान है, कोण का नहीं।

Question 114

If the ratio of supplementary and complementary angle of an angle is 5 : 2, then the value of the angle will be :

  1. A20°
  2. B60°
  3. C30°
  4. D150°

Explanation

माना कोण x है; संपूरक = 180° − x और पूरक = 90° − x। (180 − x)/(90 − x) = 5/2 से 360 − 2x = 450 − 5x, अतः 3x = 90 और x = 30°। जाँच: 150° : 60° = 5 : 2।

Question 114

In given figure PQ⊥PS, PQ||SR, ∠SQR = 28° and ∠QRT = 65°, then the value of x is

Figure: Line PQ at top, line SRT at bottom parallel to PQ, PS vertical and perpendicular to both. Angle SQR is 28 degrees and the exterior angle QRT at R is 65 degrees. Diagram added and verified: angle QSR works out to 37 degrees, so x = angle PSQ = 90 - 37 = 53 degrees, matching the stored answer.

  1. A37°
  2. B93°
  3. C53°
  4. D56°

Explanation

PQ ⊥ PS और PQ || SR, इसलिए ∠PSR = 90°। रेखा ST पर ∠QRS = 180° − 65° = 115°। त्रिभुज QSR में ∠QSR = 180° − 28° − 115° = 37°। अतः x = ∠PSQ = 90° − 37° = 53°। 37° तो ∠QSR है, x नहीं।

Practice questions

Question 1

Find the complement of a 35° angle.

  1. A45°
  2. B55°
  3. C65°
  4. D145°

Explanation

Complement = 90° − 35° = 55°.

Question 2

Find the supplement of a 112° angle.

  1. A78°
  2. B58°
  3. C68°
  4. D88°

Explanation

Supplement = 180° − 112° = 68°.

Question 3

An angle is 20° more than its complement. Find the angle.

  1. A45°
  2. B50°
  3. C55°
  4. D35°

Explanation

Let the angle = x, so its complement = 90 − x. Condition: x = (90 − x) + 20 ⇒ 2x = 110 ⇒ x = 55°.

Question 4

Two angles forming a linear pair are such that one is 4 times the other. Find both angles.

  1. A30°, 150°
  2. B36°, 144°
  3. C40°, 140°
  4. D45°, 135°

Explanation

Let the smaller angle = x, and the larger = 4x. A linear pair sums to 180°: x + 4x = 180° ⇒ 5x = 180° ⇒ x = 36°, so the angles are 36° and 144°.

Question 5

If the ratio of the supplement and the complement of an angle is 8 : 3, find the angle.

  1. A30°
  2. B36°
  3. C45°
  4. D54°

Explanation

Let the angle = x. (180 − x)/(90 − x) = 8/3 ⇒ 3(180 − x) = 8(90 − x) ⇒ 540 − 3x = 720 − 8x ⇒ 5x = 180 ⇒ x = 36°. Check: complement is 54°, supplement is 144°, and 144:54 = 8:3.

Question 6

A transversal cuts two parallel lines. If one interior angle is 65°, find its co-interior angle.

  1. A65°
  2. B115°
  3. C25°
  4. D180°

Explanation

Co-interior angles at parallel lines sum to 180°. So the other angle = 180° − 65° = 115°.

Question 7

Two lines intersect at a point. One angle is (3x + 10)° and its vertically opposite angle is (5x − 30)°. Find the value of this angle.

  1. A70°
  2. B20°
  3. C60°
  4. D80°

Explanation

Vertically opposite angles are equal: 3x + 10 = 5x − 30 ⇒ 2x = 40 ⇒ x = 20. Angle = 3(20) + 10 = 70°. Note that x = 20° is not the final answer — the angle's value, 70°, is.

Question 8

Two angles whose sum is 90° are called:

  1. Aसंपूरक कोण
  2. Bपूरक कोण
  3. Cरैखिक युग्म
  4. Dशीर्षाभिमुख कोण

Explanation

Two angles whose sum is 90° are called complementary angles.

Question 9

On a straight line, three angles x, 2x and 3x are formed on the same side. Find the largest angle.

  1. A90°
  2. B60°
  3. C30°
  4. D120°

Explanation

Angles on one side of a straight line sum to 180°: x + 2x + 3x = 180° ⇒ 6x = 180° ⇒ x = 30°. The largest angle = 3x = 90°.

Question 10

Which is the most suitable activity to teach 'vertically opposite angles are always equal' in Class 7?

  1. Aकेवल परिभाषा रटवाना
  2. Bदो पट्टियों को बीच में पिन से जोड़कर घुमाना और बने कोणों को प्रोट्रैक्टर से मापकर तुलना कराना
  3. Cकेवल पाठ्यपुस्तक पढ़वाना
  4. Dगृहकार्य में केवल प्रश्न देना

Explanation

Measuring the angles themselves with a protractor after joining two strips at a pivot and rotating them lets students discover through experience that vertically opposite angles are equal — a far more lasting lesson than rote memorisation of a definition.

Frequently asked questions

How many questions come from lines and angles in REET?+

REET 2024 had 4 questions from this topic, and it's a regular part of the Maths section every year, where most questions need to be solved by setting up an equation.

What's the difference between complementary and supplementary angles?+

Complementary angles sum to 90°, while supplementary angles sum to 180° — the two words sound similar, so it's worth memorising them separately and clearly.

Are a linear pair and supplementary angles the same thing?+

No. Every linear pair is supplementary (sum 180°), but not every supplementary pair is a linear pair — for a linear pair, the two angles must be adjacent and their non-common arms must form a straight line.

How many angles are formed when a transversal cuts two parallel lines?+

When a transversal cuts two parallel lines, 8 angles are formed in total, including pairs of corresponding, alternate interior, alternate exterior and co-interior angles — some of which are equal and some supplementary.

What's the difference between vertically opposite angles and a linear pair?+

Vertically opposite angles form directly across from each other at the intersection of two lines and are always equal, while a linear pair is a pair of adjacent angles on a single line whose sum is always 180° — both can appear in the same figure at once, but they are different definitions and shouldn't be confused.

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Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked