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Hello Math Explorer! Get ready for an exciting adventure.
Each topic has fun activities and games to help you learn. Complete all sections to learn well!
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Math Adventure Complete! 🎉
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Understanding Angles
An angle is formed when two rays meet at a common point called the vertex. We measure angles in degrees (°).
Why Learn Angles? Angles are everywhere! In architecture, art, sports, navigation, and even in nature. Understanding angles helps us build, design, and solve real-world problems.
⚡ Acute Angle
Range: 0° to 89°
Description: Sharp and narrow, less than a right angle
Description: Sharp and narrow, less than a right angle
📐 Right Angle
Range: Exactly 90°
Description: Perfect corner, like a square corner
Description: Perfect corner, like a square corner
🌊 Obtuse Angle
Range: 91° to 179°
Description: Wide and open, more than a right angle
Description: Wide and open, more than a right angle
➡️ Straight Angle
Range: Exactly 180°
Description: Forms a straight line
Description: Forms a straight line
🔄 Reflex Angle
Range: 181° to 359°
Description: Greater than straight angle, goes "the long way around"
Description: Greater than straight angle, goes "the long way around"
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Angle Architect
Welcome to Angle Architect! Click "New Problem" to start your challenge. Create the angle shown below!
🎯 Challenge: Create this angle!
Click "New Problem"
Correct!
Perfect angle!
Did You Know?
Angles are measured in degrees. A full circle is 360 degrees! Try moving the slider to explore different angles.
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Move the slider!
🎨 Drag the slider to create your angle:
Angles on a Straight Line Add Up to 180°
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Understanding the Concept
Drag the blue dots (C and D) to change the angles! Watch how they always add up to 180° because they form a straight line.
Key Concept
Angles on a straight line always sum to 180 degrees. Observe how the other angles adjust themselves so that the sum always remains 180 degrees.
Angle ABC + Angle CBD + Angle DBE = 60° + 60° + 60° = 180°
Sum of All Angles at a Point Equals 360°
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Angles Around a Point
Drag the blue dots (C, D, or E) to change the angles! Notice how all angles around point B always add up to 360° - a complete rotation!
Key Concept
Sum of all the angles at any point equals 360 degrees. This is because a complete rotation around a point is 360°!
Angle ABC + Angle CBD + Angle DBE + Angle EBA = 90° + 90° + 90° + 90° = 360°
Adjacent and Non-Adjacent Angles
Adjacent Angles: Two angles are adjacent if they share a common vertex and a common side, but do not overlap.
Non-Adjacent Angles: Angles that do not share a common side or vertex, or angles that have another angle between them.
Adjacent Angles
∠ABD and ∠DBE are adjacent angles. They share vertex B and side BD.
Non-Adjacent Angles
∠ABD and ∠FBA are not adjacent. They share vertex B but not a common side.
Supplementary Angles Add Up to 180°
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Supplementary Angles
Drag the blue dot (C) to change the angles! Watch how angle ABC and angle CBD always add up to 180° because they are supplementary.
Key Concept
Angles ABC and CBD are Supplementary since their sum equals 180 degrees. Supplementary angles always form a straight line!
Angle ABC + Angle CBD = 90° + 90° = 180°
Complementary Angles Add Up to 90°
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Complementary Angles
Drag the blue dot (C) to change the angles! Watch how angle ABC and angle CBD always add up to 90° because they are complementary.
Key Concept
Angles ABC and CBD are Complementary since their sum equals 90 degrees. Complementary angles fit together to make a right angle!
Angle ABC + Angle CBD = 60° + 30° = 90°
Vertically Opposite Angles Are Equal
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Vertically Opposite Angles
Drag the blue points to change the intersection angle. Watch how the vertically opposite angles (red-red and blue-blue) always remain equal!
Mathematical Proof
Since angles on a straight line add to 180°: ∠A + ∠B = 180° and ∠B + ∠C = 180°. Therefore ∠A = ∠C. Similarly, ∠B = ∠D.
Drag the points to see how vertically opposite angles remain equal!