Geometry in the Real World
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Geometry in the Real World
📐 Part 1: Angle Facts and Real-World Shapes
Key angle facts
Angles at a point add to 360°.
Angles on a straight line add to 180°.
Vertically opposite angles are equal.
The interior angles of a triangle add to 180°.
An exterior angle and its adjacent interior angle add to 180°.
🏗️ Part 2: Geometry in Structures and Packaging
Read each diagram description carefully. Sketch a quick diagram if it helps.
✏️ Part 3: Design Your Own Geometric Structure
✅ Answer Key
1. 360° − 110° − 85° = 165°.
2. 180° − 72° = 108°.
3. Vertically opposite angles are equal, so x = 58°. The adjacent angle is 180° − 58° = 122°, so y = 122°.
4. Triangle total: 180° − 65° − 65° = 50°. Exterior angle: 180° − 50° = 130°.
5. Exterior angle: 360° ÷ 8 = 45°. Interior angle: 180° − 45° = 135°.
6. 180° − 48° − 67° = 65°. The angles in a triangle add to 180°.
7. 360° − 90° − 90° − 75° = 105°.
8. A rectangular prism has 12 edges and 8 vertices. Example: a shoebox or cereal box.
9. A hexagon has interior angle total (6 − 2) × 180° = 720°. The known angles total 630°, so the sixth angle is 90°.
10. 180° − 128° = 52°. Adjacent angles on a straight line are supplementary.
11. Answers will vary. Check that the drawing includes three shapes, three labelled angles and a clear explanation.
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