Question

Find the sum of the interior angles of a regular polygon of 20 sides. Also find the measure of its each interior angle and each exterior angle.​

Answer 1

GIVEN :-

• Number of sides of regular polygon = 20

TO FIND :-

• Sum of interior angles .

• Measure of each interior angle .

• Measure of each exterior angle .

SOLUTION :-

$\bullet \sf \ Sum \ of \ interior \ angles = (n-2) \times 180$

                                     $= \sf (20-2) \times 180 \\\\= 18 \times 180 \\\\=\bf 3240 ^{\circ}$

$\bullet \sf \ Measure \ of \ each \ interior \ angle = \dfrac{Sum \ of \ interior \ angles }{No \ of \ sides }$

                                                 $= \sf \dfrac{3240}{20}\\\\= 162 ^\circ$

$\bullet \sf \ Measure \ of \ each \ exterior \ angle = \dfrac{360}{n}$

                                                 $= \sf \dfrac{360}{20} \\\\= 18 ^\circ$