The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.

It is given that the ratio between the number of sides of two regular polygons is 3 : 4. Let the number of sides of the first polygon be 3n and the number of sides of the second polygon be 4n. The sum of the interior angles of a polygon is (2n \- 4) x 90°. Sum of interior angles of the first polygon = (2 x 3n \- 4) x 90° = (6n \- 4) x 90° Sum of interior angles of the second polygon = (2 x 4n \- 4) x 90° = (8n \- 4) x 90° It is also given that the ratio between the sum of their interior angles is 2 : 3. By cross multiplying, we get ⇒ 3(6n \- 4) = 2(8n \- 4) ⇒ 18n \- 12 = 16n \- 8 ⇒ 18n \- 16n = 12 \- 8 ⇒ 2n = 4 ⇒ n = ⇒ n = 2 The number of sides of the first polygon is = 3n = 3 x 2 = 6 The number of sides of the second polygon is = 4n = 4 x 2 = 8 Hence, the number of sides are 6 and 8.

Two alternate sides of a regular polygon, when produced, meet at right angle. Calculate the number of sides in the polygon.

View Answer Bookmark Now

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED

View Answer Bookmark Now

Three of the exterior angles of a hexagon are 40°, 51° and 86°. If each of the remaining exterior angles is x°, find the value of x.

View Answer Bookmark Now

Calculate the number of sides of a regular polygon if:
(i) its interior angle is five times its exterior angle.
(ii) the ratio between its exterior angle and interior angle is 2 : 7.
(iii) its exterior angle exceeds its interior angle by 60°.

View Answer Bookmark Now

Mathematics

The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.

Geometrical Shapes

Related Questions

Two alternate sides of a regular polygon, when produced, meet at right angle. Calculate the number of sides in the polygon.

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED

Three of the exterior angles of a hexagon are 40°, 51° and 86°. If each of the remaining exterior angles is x°, find the value of x.

Calculate the number of sides of a regular polygon if:
(i) its interior angle is five times its exterior angle.
(ii) the ratio between its exterior angle and interior angle is 2 : 7.
(iii) its exterior angle exceeds its interior angle by 60°.

Mathematics

The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.

Geometrical Shapes

Related Questions

Two alternate sides of a regular polygon, when produced, meet at right angle. Calculate the number of sides in the polygon.

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:(i) ∠BAE(ii) ∠ABE(iii) ∠BED

Three of the exterior angles of a hexagon are 40°, 51° and 86°. If each of the remaining exterior angles is x°, find the value of x.

Calculate the number of sides of a regular polygon if:(i) its interior angle is five times its exterior angle.(ii) the ratio between its exterior angle and interior angle is 2 : 7.(iii) its exterior angle exceeds its interior angle by 60°.

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED

Calculate the number of sides of a regular polygon if:
(i) its interior angle is five times its exterior angle.
(ii) the ratio between its exterior angle and interior angle is 2 : 7.
(iii) its exterior angle exceeds its interior angle by 60°.