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SSC CGL Angles & Lines

Study Material — 3 PYQs (2018–2020) · Concept Notes · Shortcuts

SSC CGL Angles & Lines is a frequently tested subtopic — 3 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.

3 PYQs
2018–2020
41 Practice
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8 Key Points
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Previous Year Questions

SSC CGL Angles & Lines — Past Exam Questions

3 questions from actual SSC CGL papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

Two lines intersect each other. If one of the angles formed at the intersection is 65°, what is the measure of its vertically opposite angle?

Exam Q 22020Previous Year Pattern

Two lines intersect each other. One of the angles formed is 65°. What is the measure of the angle adjacent to it on a straight line?

Exam Q 32020Previous Year Pattern

Two straight lines intersect each other. One of the angles formed is 35°. A third line is drawn parallel to one of the intersecting lines. If this third line intersects the second line, what is the measure of the acute angle between the third line and the second line?

Concept Notes

Angles & Lines— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic
Key angle types include

Acute angles (less than 90°), Right angles (exactly 90°), Obtuse angles (90° to 180°), Straight angles (180°), Reflex angles (180° to 360°), and Complete angles (360°). Adjacent angles share a common vertex and side. Complementary angles add up to 90°. Supplementary angles add up to 180°. When parallel lines are cut by a transversal, several angle pairs are formed.

Corresponding angles are equal. Alternate interior angles are equal. Alternate exterior angles are equal. Co-interior angles are supplementary (add to 180°).

These properties solve most line-angle problems in SSC. Vertically opposite angles are always equal when two lines intersect. Linear pairs always add to 180°. When multiple angles meet at a point, they sum to 360°

Formulas to remember

Sum of interior angles of n-sided polygon = (n-2) × 180°. Each interior angle of regular polygon = (n-2) × 180° ÷ n. Each exterior angle of regular polygon = 360° ÷ n

SSC typically asks

Find missing angles using given relationships. Identify angle types in geometric figures. Calculate angles in polygons. Solve problems involving parallel lines and transversals.

Questions often combine angle properties with triangle or quadrilateral concepts.

2.Shortcuts

Use these to save 30–60 seconds per question

For parallel line problems, remember CAIA rule - Corresponding, Alternate Interior, Alternate Exterior angles are Always equal. Co-interior angles Always add to 180°. This eliminates confusion during exams.

3.Worked Example

Solve this step-by-step before moving on
1
Step 1

Co-interior angles are supplementary (add to 180°)

2
Step 2

Let the co-interior angle be x

3
Step 3

65° + x = 180°

4
Step 4

x = 180° - 65° = 115° Answer: 115° Another Shortcut: When solving polygon angle problems, use the quick formula: Interior angle = 180° - (360° ÷ n). This saves calculation time.

4.Exam Traps

Common mistakes students make — avoid these

Students often confuse corresponding angles with co-interior angles. Remember - corresponding angles are EQUAL, co-interior angles are SUPPLEMENTARY. Also, many forget that exterior angles of any polygon always sum to 360°, regardless of the number of sides. Practice identifying angle relationships quickly.

Most SSC questions test basic properties rather than complex proofs. Focus on recognizing patterns and applying formulas accurately.

Key Points to Remember

  • Complementary angles add to 90°, supplementary angles add to 180°
  • Vertically opposite angles are always equal when two lines intersect
  • Corresponding and alternate angles are equal when parallel lines are cut by transversal
  • Co-interior angles are supplementary (add to 180°) in parallel line systems
  • Linear pair of angles always sums to 180°
  • Sum of interior angles of n-sided polygon = (n-2) × 180°
  • Each exterior angle of regular polygon = 360° ÷ n
  • All angles around a point sum to 360°

Exam-Specific Tips

  • Sum of all exterior angles of any polygon is always 360°
  • Each interior angle of regular hexagon is 120°
  • Each interior angle of regular octagon is 135°
  • Straight angle measures exactly 180°
  • Complete angle measures exactly 360°
  • Sum of interior angles of triangle is 180°
  • Sum of interior angles of quadrilateral is 360°
  • Each interior angle of square is 90°
Practice MCQs

Angles & Lines — Practice Questions

41graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 41

All MCQs →
Practice 1easy

An exterior angle of a triangle is 110°. If the two non-adjacent interior angles are in the ratio 3:2, what is the measure of the larger non-adjacent interior angle?

Practice 2easy

Two complementary angles are in the ratio 1:5. What is the measure of the smaller angle?

Practice 3easy

Three angles of a triangle are in the ratio 2:3:4. What is the measure of the largest angle?

Practice 4easy

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the measure of the other alternate interior angle?

Practice 5easy

Two complementary angles are in the ratio 1:5. What is the measure of the smaller angle?

Practice 6easy

A line makes an angle of 35° with the horizontal. What is the angle it makes with the vertical?

Practice 7easy

Two parallel lines are cut by a transversal. If one of the alternate interior angles is 72°, what is the other alternate interior angle?

Practice 8easy

At an intersection of two straight lines, one angle is 4 times another angle. What is the measure of the smaller angle?

Practice 9easy

A line makes an angle of 35° with the horizontal. What is the angle it makes with the vertical?

Practice 10easy

Two lines intersect each other. One of the angles formed is 65°. What is the measure of the angle adjacent to it on a straight line?

Practice 11easy

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the measure of the other alternate interior angle?

Practice 12easy

Two lines intersect each other. If one of the angles formed is 65°, what is the measure of the angle adjacent to it on a straight line?

Practice 13easy

Three lines meet at a point. The angles formed are in the ratio 2:3:4. What is the measure of the largest angle?

Practice 14easy

Two parallel lines are cut by a transversal. If one of the alternate interior angles is 72°, what is the measure of the corresponding angle on the same side of the transversal?

Practice 15easy

Two lines intersect each other. If one of the angles formed is 65°, what is the measure of the angle adjacent to it on a straight line?

Practice 16easy

If two supplementary angles are in the ratio 4:5, what is the measure of the larger angle?

Practice 17medium

A straight line makes an angle of 30° with the positive x-axis. Another line perpendicular to this line makes an angle of θ with the positive x-axis. What is the value of θ (taking the acute angle)?

Practice 18medium

In a triangle, one exterior angle measures 140°. The two non-adjacent interior angles are in the ratio 3:4. What is the measure of the smaller of these two non-adjacent interior angles?

Practice 19medium

Two lines intersect such that one of the angles formed is 65°. If a third line is drawn parallel to one of the original lines and passes through the point of intersection, what is the measure of the acute angle between this third line and the second original line?

Practice 20medium

Two parallel lines are cut by a transversal. If one of the alternate interior angles is 72°, what is the measure of the other alternate interior angle?

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60-Second Revision — Angles & Lines

  • Remember: CAIA rule for parallel lines - Corresponding, Alternate angles Equal, Co-interior Supplementary
  • Formula: Interior angles sum = (n-2) × 180° for n-sided polygon
  • Trap: Don't confuse corresponding angles (equal) with co-interior angles (supplementary)
  • Quick check: Exterior angles of any polygon always sum to 360°
  • Remember: Vertically opposite angles are always equal
  • Formula: Each exterior angle of regular polygon = 360° ÷ n
  • Key: Linear pairs and supplementary angles both add to 180°
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