Angle Rules

Explore the relationships between angles that are complementary (add to 90°), supplementary (add to 180°), at a point (add to 360°), and at an intersection. Use the controls to create and solve angle problems.

This interactive demonstration allows you to explore four fundamental rules of geometry in a hands-on way. Grab and drag the circular handles on the lines to watch angle values update in real-time, providing instant visual proof that these mathematical relationships always hold true.

How to Use

Interactive Exploration

Grab and drag the circular handles on the lines to change their positions and watch the angle values update in real-time. This provides instant visual proof of the geometric rules: no matter how you adjust the lines, the mathematical relationships will always hold true.

Tab Navigation

Switch between the four fundamental angle concepts:

• O Tab: Explore angles at a point (sum to 360°)
• L Tab: Investigate complementary angles (sum to 90°)
• — Tab: Study supplementary angles on a straight line (sum to 180°)
• X Tab: Discover vertically opposite angles at intersections (equal pairs)

Control Your Learning

Use the Total Angles slider to add or remove lines and create more complex problems. Each tab has different limits based on the geometric concept being explored.

Generate new challenges with the Randomize button to create fresh angle problems, or use Equalize to make all angles equal in size for easier analysis.

Test Your Understanding

Click on the question mark labels to reveal or hide the angle values. These interactive reveal buttons help you practice solving problems before checking your answers:

• a = ? reveals the unknown angle value
• Total = ? reveals the sum of all angles
• Additional angle labels for intersecting lines (b = ?, c = ?)

Visual Aids

Toggle helpful visual guides with the protractor and circle buttons to better understand angle measurements and relationships.

Choose your preferred Paper Style background to customize your learning environment with grid lines, dots, isometric patterns, or a clean background.

Educational Outcome

As you manipulate the interactive elements, you’ll build a strong, intuitive understanding of these core geometric principles. The dynamic exploration demonstrates that:

• Angles at a Point: No matter how you arrange the lines, angles around a central point always sum to 360°
• Complementary Angles: Adjacent angles forming a right angle always total 90°
• Supplementary Angles: Adjacent angles on a straight line always sum to 180°
• Vertically Opposite Angles: At an intersection, opposite angles are always equal

This hands-on approach helps transform abstract geometric rules into concrete, visual understanding that builds mathematical confidence. 📐✨