If the interior angle of a regular polygon is double the exterior angle, 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

Open in App

Solution

The correct option is D
6

Let exterior angle $(e) = x^{\circ}$

$∴$ Interior angle $(i) = 2 x^{\circ}$

i+e= $180^{\circ}$

$2 x + x = 180^{\circ}$

$3 x = 180^{\circ}$

$x = 60^{\circ}$

$∴ e = 60^{\circ}$

$n = \frac{360}{e}$

$= \frac{360}{60}$

=6

Suggest Corrections

Similar questions

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

The exterior angle of a regular polygon is one – third of its interior angle. How many sides has the polygon?

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

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°. The measure of each interior angle of a regular polygon which has double the number of sides as the first polygon is

Join BYJU'S Learning Program

If the interior angle of a regular polygon is double the exterior angle, the polygon has ___sides.

The correct option is D 6 Let exterior angle (e)=x∘ ∴ Interior angle (i)=2x∘ i+e=180∘ 2x+x=180∘ 3x=180∘ x=60∘ ∴e=60∘ n=360e =36060 =6

The correct option is D
6

Let exterior angle $(e) = x^{\circ}$

$∴$ Interior angle $(i) = 2 x^{\circ}$

i+e= $180^{\circ}$

$2 x + x = 180^{\circ}$

$3 x = 180^{\circ}$

$x = 60^{\circ}$

$∴ e = 60^{\circ}$

$n = \frac{360}{e}$

$= \frac{360}{60}$

=6