Question

The ratio between an exterior angle and an Interior angle of a regular polygon is 2 : 3. Find the number of sides in a polygon.

Answer 1

Let the meet of ratio of angles be x.

Hence 2x + 3x = 180°

=) 5x = 180°

=) x = 180°/5
= 36°.

Hence interior angle = 3*36°
= 108°

Since measure of an angle in regular polygon,

=) 108 = [(n-2)* 180] / n

=) 108n = 180n - 360°

=) 180n - 108n = 360°

=) 72n = 360°

=) n = 360/72

= 5 sides.

Hope it's helpful to u.

Answer 2

Answer:

Step-by-step explanation:Hence 2x + 3x = 180°

=) 5x = 180°

=) x = 180°/5

= 36°.

Hence interior angle = 3*36°

= 108°

Since measure of an angle in regular polygon,

=) 108 = [(n-2)* 180] / n

=) 108n = 180n - 360°

=) 180n - 108n = 360°

=) 72n = 360°

=) n = 360/72

= 5 sides.

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