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| Answer» <html><body><p><strong>Step-by-step explanation:</strong></p><h2><u>Given </u><u>:</u><u>-</u></h2><p>A regular polygon has 18 <a href="https://interviewquestions.tuteehub.com/tag/sides-1207029" style="font-weight:bold;" target="_blank" title="Click to know more about SIDES">SIDES</a> </p><h2><u>To </u><u>find</u><u>:</u><u>-</u></h2><p>i) Find the measure of its <a href="https://interviewquestions.tuteehub.com/tag/exterior-447186" style="font-weight:bold;" target="_blank" title="Click to know more about EXTERIOR">EXTERIOR</a> angle ?</p><p>ii) Find the <a href="https://interviewquestions.tuteehub.com/tag/number-582134" style="font-weight:bold;" target="_blank" title="Click to know more about NUMBER">NUMBER</a> of its diagonals ?</p><h2><u>Solution</u><u> </u><u>:</u><u>-</u></h2><p>Given that :</p><p>The number of sides in a regular polygon (n) = 18</p><p>We know that</p><p>The measure of each exterior angle of a regular polygon of 'n' sides is 360°/n</p><p>Each exterior angle of the given regular polygon of 18 sides </p><p>=> 360°/18</p><p>=> 20°</p><p>The measure of the exterior angle = 20°</p><p>and</p><p>We know that</p><p>The number of diagonals of a regular polygon of'n'sides is n(n-3)/2</p><p>On Substituting the <a href="https://interviewquestions.tuteehub.com/tag/value-1442530" style="font-weight:bold;" target="_blank" title="Click to know more about VALUE">VALUE</a> of n in the above formula then</p><p>=> (18)(18-3)/2</p><p>=> 18×15/2</p><p>=> 9×15</p><p>=> 135</p><p>The number of diagonlos = 135</p><h2><u>Answer</u><u>:</u><u>-</u></h2><p>I) The measure of the exterior angle of the given regular polygon = 20°</p><p>ii) The number of diagonals of the given regular polygon = 135</p><h2><u>Used </u><u>formulae</u><u>:</u><u>-</u></h2><ul><li>The measure of each exterior angle of a regular polygon of 'n' sides is 360°/n</li><li>The number of diagonals of a regular polygon of'n'sides is n(n-3)/2</li><li>n = Number of sides in the given regular polygon</li></ul></body></html> | |