29. The exterior angle of regular polygon is onethird of its interior

1.	29. The exterior angle of regular polygon is onethird of its interior angle, how many sides hasthe polygon.
Answer» Let number of sides in polygon be n Interior angle = (n - 2)/n180Exterior angle = 180 - interior angle As per given conditionExterior angle = 1/3 interior angle180 - interior angle = 1/3 interior angle4/3 interior angle = 180Interior angle = 135 Hence,(n - 2)/n 180 = 135180n - 360 = 135n45n = 360n = 360/45 = 8 Therefore, Number of sides are 8

29. The exterior angle of regular polygon is onethird of its interior angle, how many sides hasthe polygon.

Answer»

Let number of sides in polygon be n

Interior angle = (n - 2)/n*180Exterior angle = 180 - interior angle

As per given conditionExterior angle = 1/3 interior angle180 - interior angle = 1/3 interior angle4/3 interior angle = 180Interior angle = 135

Hence,(n - 2)/n * 180 = 135180n - 360 = 135n45n = 360n = 360/45 = 8

Therefore, Number of sides are 8