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📐 Angles

Ngā Koki — Measuring Turns

🔄 What is an Angle?

An angle is formed where two lines meet. We measure angles in degrees (°). A full turn is 360°, half turn is 180°, and quarter turn is 90°.

📊 Types of Angles

< 90°
Acute

Less than 90°

= 90°

Right

Exactly 90°

> 90°

Obtuse

Between 90° and 180°

= 180°

Straight

Exactly 180° (a line)

> 180°

Reflex

Between 180° and 360°

📏 Measuring with a Protractor

Steps

  1. Place the protractor's centre point on the angle's vertex (point)
  2. Line up the baseline with one arm of the angle
  3. Read where the other arm crosses the scale
  4. Use the correct scale (inner or outer) starting from 0°

📐 Angle Rules

Useful Facts
  • Angles on a straight line = 180°
  • Angles around a point = 360°
  • Angles in a triangle = 180°
  • Angles in a quadrilateral = 360°
  • Vertically opposite angles are equal

💡 Worked Example

Finding Missing Angles

If one angle on a straight line is 65°, what is the other?

Solution: 180° - 65° = 115°

✏️ Activities

Name the Angle Type
  1. 45° = ___________ angle
  2. 90° = ___________ angle
  3. 120° = ___________ angle
  4. 200° = ___________ angle

Calculate Missing Angles

  1. On a straight line: 70° + ? = 180° → ? = ___°
  2. In a triangle: 50° + 60° + ? = 180° → ? = ___°

My working:

👩‍🏫 Teacher Notes

Curriculum Links

  • Mathematics: Geometry & Measurement — angles