Let 3a=interior angle and 2a=exterior angleWe know thatinterior angle +exterior angle=180°⇒3a+2a=180°⇒5a=180°⇒a=36°So, exterior angle=2×36°=72°For a regular polygon of n sides,each exterior angle has a measure of 360nSince the exterior angle of each angle has a measure of 72° , then the number of sides nn=360°72°=5 sides

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Let 3 a = interior angle and 2 a = exterior angle We know that interior angle + exterior angle = 180 ° \Rightarrow 3 a + 2 a = 180 ° \Rightarrow 5 a = 180 ° \Rightarrow a = 36 ° So, exterior angle = 2 \times 36 ° = 72 ° For a regular polygon of n sides, each exterior angle has a measure of \frac{360}{n} Since the exterior angle of each angle has a measure of 72 °, then the number of sides n n = \frac{360 °}{72 °} = 5 side s .

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