Curriculum

Course: Mathematics — Second Preparatory

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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

Interior and Exterior Angles of a Polygon

Mathematics — Second Preparatory

Interior and Exterior Angles of a Polygon

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Find the sum of the interior angles of a pentagon. If it is regular find the measure of each angle	Findinterioranglespentagon
Solution	The sum = (5 − 2) × 180 = 540°. If the pentagon is regular each angle = 540 ÷ 5 = 108°	pentagonregularangle
Example 2	Find the interior angle of a regular octagon	Findinteriorangleregular
Solution	The sum = (8 − 2) × 180 = 1080° and each angle = 1080 ÷ 8 = 135°. Check: the exterior angle is 45° and 135 + 45 = 180	1080angleCheckexterior
Example 3	A polygon has interior angles that add up to 1440°. Find the number of its sides	polygoninteriorangles1440
Solution	(n − 2) × 180 = 1440 so n − 2 = 8 and n = 10. The polygon is a decagon	1440polygondecagon
Example 4	A regular polygon has an exterior angle of 24°. Find the number of its sides then find its interior angle	regularpolygonexteriorangle

Solution→The number of sides = 360 ÷ 24 = 15. The interior angle = 180 − 24 = 156°. Check: (15 − 2) × 180 ÷ 15 = 13 × 180 ÷ 15 = 156.

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