Question

The ratio between the exterior angle and the interior angle of a regular polygon is 2 ratio 7.Find the number of sides in the polygon.

Answer 1

Hey mate!!!!

Exterior angle + interior angle = 180°

Let them be 2x and 7x
so we have 7x + 2x = 180°
9x = 180°
x = 180/9
x = 20°
Interior angle is 7x = 7 × 20 = 140°



Now using the formula for finding angles of a regular polygon
(n-2) × 180° = sum of all angles
where n is the side
so

sum of all angles = 140n

using the formula we have
$(n - 2) \times 180 = 140n \\ 180n - 360 = 140n \\ \\ 180n - 140n = 360 \\ 40n = 360 \\ n = \frac{360}{40} \\ n = 9$
The polygon has 9 sides.


Hope it helps dear friend ☺️✌️

Answer 2

Answer:

There are 9 sides in the polygon