Answer:
option B is correct
interior angle of given polygon =156
exterior angle of polygon=180 - 156 =24
as we know that sum of exterior angle of any polygon is 360 degree
so number of sides of regular polygon=360/24=15
Answer:
option B. 15
Step-by-step explanation:
Sum of interior angles of a polygon with n sides = ( n - 2 ) x 180°
Therefore each interior angle,
[tex]\frac{n - 2}{n} \times 180^\circ[/tex]
Given the interior angles = 156°
That is ,
[tex](\frac{n-2}{n}) \times 180 = 156\\\\\frac{n-2}{n} = \frac{156}{180}\\\\1- \frac{2}{n} = \frac{156}{180}\\\\1 - \frac{156}{180} = \frac{2}{n}\\\\\frac{180-156}{180} = \frac{2}{n}\\\\\frac{24}{180} = \frac{2}{n}\\\\24 \times n = 2 \times 180\\\\n = \frac{2 \times 180}{24} =\frac{180}{12} = 15[/tex]
