Curriculum

Course: Mathematics — First Preparatory

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Curriculum

Mathematics — First Preparatory

Unit 1: Numbers

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Unit 2: Algebra

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Unit 3: Statistics

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Unit 4: Geometry

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Text lesson

Polygons

Mathematics — First Preparatory

Polygons

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Find the sum of the interior angles of an octagon	Findinterioranglesoctagon
Solution	n = 8 so the sum = (8 − 2) × 180 = 6 × 180 = 1080°	1080
Example 2	Find the interior angle of a regular hexagon	Findinteriorangleregular
Solution	The sum of the angles = (6 − 2) × 180 = 720° and each angle = 720 ÷ 6 = 120°	anglesangle
Example 3	The sum of the interior angles of a polygon is 1440°. How many sides does it have?	interioranglespolygon1440
Solution	(n − 2) × 180 = 1440 so n − 2 = 8 and n = 10. The polygon is a decagon	1440polygondecagon
Example 4	Each interior angle of a regular polygon is 150°. Find the number of sides	interiorangleregularpolygon
Solution	The exterior angle = 180 − 150 = 30°. So n = 360 ÷ 30 = 12 sides. The polygon is a dodecagon	exterioranglesidespolygon

Key points

Example 5 (the hardest)Find the number of diagonals of a decagon.

SolutionThe number of diagonals = 10 × (10 − 3) ÷ 2 = 10 × 7 ÷ 2 = 35 diagonals.

Polygons · 3 / 5