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Question
The ratio between the interior angle and the exterior angle of a regular polygon is 2: 1. Find:
(i) each exterior angle of the polygon ;
(ii) number of sides in the polygon.
Solution
Interior angle : exterior angle = 2 : 1
Let interior angle = 2x° & exterior angle = x°
∴ 2x° + x° = 180°
3x = 180°
x = 60°
∴ Each exterior angle = 60°
Let no.of. sides = n
`(360°)/"n" = 60°`
n = `(360°)/(60°)`
n = 6
∴ (i) x = 60° (ii) 6
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Fill in the blanks :
In case of regular polygon, with :
| No.of.sides | Each exterior angle | Each interior angle |
| (i) ___8___ | _______ | ______ |
| (ii) ___12____ | _______ | ______ |
| (iii) _________ | _____72°_____ | ______ |
| (iv) _________ | _____45°_____ | ______ |
| (v) _________ | __________ | _____150°_____ |
| (vi) ________ | __________ | ______140°____ |
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