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Rotation Series

Rotation Series problems present a sequence of identical or similar shapes that rotate by a fixed angle at each step. The rotation can be clockwise or anticlockwise, with common step angles including 15°, 30°, 45°, 60°, 90°, and 180°. You must determine the rotation pattern and identify the next figure in the series.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Rotation Series

Rotation Series problems present a sequence of identical or similar shapes that rotate by a fixed angle at each step. The rotation can be clockwise or anticlockwise, with common step angles including 15°, 30°, 45°, 60°, 90°, and 180°. You must determine the rotation pattern and identify the next figure in the series.

Prerequisites

Understanding of degrees in a circle (360°) Concept of clockwise vs anticlockwise rotation Basic geometry of common shapes Pattern recognition skills
Why This Matters: Rotation Series problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test understanding of angular progression and spatial transformation.

How to Solve Rotation Series Problems

1

Step 1: Identify the shape in the series (triangle, arrow, diamond, etc.)

2

Step 2: Calculate the rotation angle between consecutive figures

3

Step 3: Determine if the rotation is clockwise or anticlockwise

4

Step 4: Verify the rotation step is constant throughout the series

5

Step 5: Apply the same rotation step to the last figure to find the next

6

Step 6: If rotation exceeds 360°, subtract 360° to get the effective angle

7

Step 7: Select the option with the correct rotation

Pro Strategy: Calculate the angle difference between the first and second figure, then between second and third to confirm consistency. Apply the same angular increment to the last figure to find the next orientation.

Example Problem

Example: A triangle rotates by 45° clockwise each step: 0°, 45°, 90°, 135°, ___. Find the next rotation angle. Solution: Step 1: Shape = triangle Step 2: Rotation step = 45° clockwise Step 3: Last angle = 135° Step 4: Next angle = 135° + 45° = 180° Answer: Triangle rotated 180°

Pro Tips & Tricks

  • Common rotation steps: 15°, 30°, 45°, 60°, 90°, 120°, 180°
  • A 90° clockwise rotation is equivalent to 270° anticlockwise
  • Arrows and triangles are commonly used for rotation series
  • If rotation is not consistent between all pairs, check for alternating patterns
  • The shape's appearance (filled/unfilled) usually remains constant
  • Draw the shape rotated by the step angle to visualize the next figure

Shortcut Methods to Solve Faster

Rotation step = Angle(Figure₂) - Angle(Figure₁)
Next angle = Last angle + Step angle (mod 360)
If step = 90°, the shape faces next cardinal direction (up→right→down→left)
If step = 45°, the shape moves to intercardinal directions

Common Mistakes to Avoid

Miscalculating the rotation angle between figures
Confusing clockwise with anticlockwise rotation
Forgetting to apply modulo 360° when angle exceeds 360°
Assuming rotation when the pattern might be reflection or movement

Exam Importance

Rotation Series is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
INSURANCE
2-3 questions

Ready to Master Rotation Series?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now