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in a regular polygon, each interior angle is twice the exterior angle. the number of sides of the polygon is _________​

Answer» <html><body><p><strong>Answer:</strong></p><h2><strong><a href="https://interviewquestions.tuteehub.com/tag/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</a> or OCTAGON</strong></h2><p><strong>Step-by-step explanation:</strong></p><p><strong>Concept : Sum of Interior angle + Sum of Exterior angle = 180°</strong></p><p><strong></strong></p><p><strong>Let the interior angle be 'x'</strong></p><p><strong></strong></p><p><strong>=&gt; Exterior angle = <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a> * Interior angle = 3 x</strong></p><p><strong></strong></p><p><strong>=&gt; x + 3x = 180°</strong></p><p><strong></strong></p><p><strong>=&gt; 4x = 180°</strong></p><p><strong></strong></p><p><strong>=&gt; x = 180 / <a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a></strong></p><p><strong></strong></p><p><strong>=&gt; x = 45°</strong></p><p><strong></strong></p><p><strong>We also know that,</strong></p><p><strong></strong></p><p><strong>Exterior angle = 360° / n</strong></p><p><strong></strong></p><p><strong>Where n represents the number of sides of a polygon.</strong></p><p><strong></strong></p><p><strong>=&gt; n = 360° / Exterior angle</strong></p><p><strong></strong></p><p><strong>=&gt; n = 360° / 45°</strong></p><p><strong></strong></p><p><strong>=&gt; n = 8</strong></p><p><strong></strong></p><p><strong>Hence it is a 8 sided polygon which is an octagon.</strong></p></body></html>


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