If the interior angle of a regular polygon is double the exterior angle, then the polygon has ______ sides.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
6

It is given that the polygon is regular.

Let exterior angle = e°

Interior angle = 2e° (given)

In a regular polygon,

interior angle + exterior angle = 180°

2e + e = 180°

3e = 180°

e = 60°

Number of sides (n) = $\frac{360 °}{exterior angle}$

= $\frac{360 °}{60 °}$

= 6

Suggest Corrections

Similar questions

If the ratio of the exterior angle and interior angle of a regular polygon is 2: 3, the the polygon has ____ sides.

Q. Each interior angle of a regular polygon is

144^{0}

. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.

Each interior angle of a regular polygon is $144^{\circ}$ . Then the measure of each interior angle of a regular polygon which has double the number of sides as the first polygon is

Q. Each interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon.

Q. The interior angle of a regular polygon with

n

sides is

6

times that of an exterior angle of a regular polygon with

\frac{3}{2} n

sides. Then

n

equals

Join BYJU'S Learning Program

If the interior angle of a regular polygon is double the exterior angle, then the polygon has ______ sides.

The correct option is C 6 It is given that the polygon is regular. Let exterior angle = e° Interior angle = 2e° (given) In a regular polygon, interior angle + exterior angle = 180° 2e + e = 180° 3e = 180° e = 60° Number of sides (n) = 360°exterior angle = 360°60° = 6