Q. 43.6( 5 Votes )

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Answer :

Let x be the measure of inner angle and 2x be the measure of outer angle.

Assume that the regular polygon has n sides (or angles)


Sum of the interior angles = (n – 2) × 180°


n × x = (n – 2) × 180°


nx = (n – 2) × 180° … (1)


Sum of the exterior angle = 360°


n × 2x = 360°


2nx = 360°



Substitute this value for x in equation (1)



180° = 180°n – 360°


180° = 180°n – 360°


180°n = 180° + 360°


180°n = 540°



n = 3


Sum of the angles of n-sided polygon = (n – 2) × 180°


S = (3 – 2) × 180°


S = 1 × 180°


S = 180°


Measure of each interior angle



i. Measure of each interior angle is 60°


ii. Number of sides of this polygon is 3.


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