4.2

Angles in polygons

9 flashcards to master Angles in polygons

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Key Concept Flip

What is the sum of the interior angles of a hexagon?

Answer Flip

The sum of interior angles of an n-sided polygon is (n-2) * 180°. For a hexagon (n=6), the sum is (6-2) * 180° = 720°.

Definition Flip

Define a regular polygon and give an example.

Answer Flip

A regular polygon has all sides and all angles equal.

Example: A square is a regular quadrilateral and an equilateral triangle is a regular triangle.
Key Concept Flip

Calculate the size of each interior angle in a regular pentagon.

Answer Flip

The sum of interior angles in a pentagon is (5-2) * 180° = 540°. Each interior angle in a *regular* pentagon is 540° / 5 = 108°.

Key Concept Flip

What is the sum of the exterior angles of *any* polygon?

Answer Flip

The sum of the exterior angles of *any* polygon (regular or irregular) is always 360 degrees. Each exterior angle is formed by extending one side of the polygon.

Key Concept Flip

If an interior angle of a regular polygon is 150°, how many sides does the polygon have?

Answer Flip

Each exterior angle is 180° - 150° = 30°. Since the sum of exterior angles is 360°, the polygon has 360° / 30° = 12 sides.

Key Concept Flip

Explain the relationship between interior and exterior angles at a vertex of a polygon.

Answer Flip

At each vertex, the interior angle and the exterior angle are supplementary, meaning they add up to 180°. The exterior angle is formed by extending one side.

Definition Flip

Define an irregular polygon and give an example.

Answer Flip

An irregular polygon is a polygon where the sides and angles are not all equal. A rectangle is an irregular polygon if its sides are not equal in length (i.e., it is not a square).

Key Concept Flip

A quadrilateral has angles 70°, 80°, and 120°. What is the size of the fourth angle?

Answer Flip

The sum of angles in a quadrilateral is 360°. Therefore, the fourth angle is 360° - (70° + 80° + 120°) = 360° - 270° = 90°.

Key Concept Flip

What formula gives the sum of the interior angles of an n-sided polygon?

Answer Flip

The formula to calculate the sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees.

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4.1 Angles 4.3 Parallel lines

Key Questions: Angles in polygons

Define a regular polygon and give an example.

A regular polygon has all sides and all angles equal.

Example: A square is a regular quadrilateral and an equilateral triangle is a regular triangle.
Define an irregular polygon and give an example.

An irregular polygon is a polygon where the sides and angles are not all equal. A rectangle is an irregular polygon if its sides are not equal in length (i.e., it is not a square).

About Angles in polygons (4.2)

These 9 flashcards cover everything you need to know about Angles in polygons for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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