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Question
Find the degree and radian measure of exterior and interior angle of a regular Heptagon.
Solution
Septagon:
We know that the sum of the measures of the exterior angles of a polygon is 360°. The measures of the interior angles of a regular polygon are equal. Hence, the measures of the exterior angles of a regular polygon are also equal.
Number of sides = 7
Number of exterior angles = 7
∴ Measure of an exterior angle of a regular heptagon = `(360°)/"no. of sides"`
= `(360°)/7`
= (51.43)°
= `(360/7 × π/180)^"c"`
= `((2π)/7)^"c"`
The sum of the measures of an interior angle and an exterior angle of a regular polygon = 180°.
∴ Measure of an interior angle of regular heptagon = `180° - (360/7)^circ`
= `((1260 - 360)/7)^circ`
= `(900/7)^circ`
= (128.57)°
= `(900/7 × π/180)^"c"`
= `((5π)/7)^"c"`
Hence, the exterior and interior angle of a regular heptagon are (51.43)° or `((2π)/7)^"c" "and" (128.57)° or ((5π)/7)^"c"`.
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