Q13 of 59 Page 195

Measurement of each of 5 interior angle is 172° and measurement of each of the other interior angle of polygon is 160°. Let’s write number of sides of the polygon.

Given:

Measure of each 5 angles = 172°


Measure of each remaining angles = 160°


Let the total number of sides for polygon be n.


Sum of all angles in given polygon = (5 × 172) + (n – 5) × 160


(5 × 172) + (n – 5) × 160 = (2n – 4) × 90


860 + 160n – 800 = (2n – 4) × 90


160n + 60 = 180n – 360


180n – 160n = 360 + 60


20n = 420


n = 420 / 20


n = 21


Therefore the given polygon has total number of sides equal to 21.


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