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Angles in parallel lines and polygons
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When a line crosses two parallel lines, it makes pairs of angles with special links. Triangles then unlock the angles of any polygon.
Parallel lines
A line crossing two parallel lines is called a transversal.
Alternate angles are equal (a Z shape).
Corresponding angles are equal (an F shape).
Co-interior angles add up to 180° (a C shape).
Alternate angles are equal (a Z shape).
Corresponding angles are equal (an F shape).
Co-interior angles add up to 180° (a C shape).
Angles in polygons
A polygon with n sides splits into (n − 2) triangles.
Sum of interior angles = (n − 2) × 180°.
Hexagon: (6 − 2) × 180° = 720°.
Sum of interior angles = (n − 2) × 180°.
Hexagon: (6 − 2) × 180° = 720°.
Regular polygons
All sides and all angles are equal.
The exterior angles of any polygon add up to 360°, so each exterior angle of a regular polygon is 360° ÷ n.
Interior angle + exterior angle = 180°.
The exterior angles of any polygon add up to 360°, so each exterior angle of a regular polygon is 360° ÷ n.
Interior angle + exterior angle = 180°.
Find the interior angle of a regular octagon.
- Exterior angle: 360° ÷ 8 = 45°
- Interior angle: 180° − 45°
Answer: 135°
Alternate and corresponding angles are equal; co-interior angles add to 180°. Interior angles sum to (n − 2) × 180°. Exterior angles of a regular polygon are 360° ÷ n.
The interactive lesson includes the diagrams for this topic.
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