Question

The interior angles of a hexagon are in the ratio 1:3:5:7:9:11. Find the largest angles​

Answer 1

Answer:

Largest angle = 220°

Step-by-step explanation:

Given , the angles of a Hexagon ABCDEF are in the ratio 1:3:5:7:9:11

Let ∠A = 1x  ∠B = 3x  ∠C = 5x  ∠D = 7x ∠E = 9  ∠F = 11

In a quadrilateral ∠A+∠B+∠C+∠D+∠E+∠F= 720°

⇒ 1x + 3x + 5x + 7x + 9x + 11x = 720°

⇒ 36x = 720

⇒ x = 720 ÷ 36 = 20

So , the angles of the hexagon is

∠A = (1 × 20)° = 20°

∠B = (3 × 20)° = 60°

∠C = (5 × 20)° = 100°

∠D = (7 × 20)° = 140°

∠E = (9 × 20)° = 180°

∠F = (11 × 20)° = 220°

Answer 2

Solution!!

The interior angles of a hexagon are given in the ratio 1:3:5:7:9:11. We have to calculate the largest angle of the hexagon.

Let the angles be x, 3x, 5x, 7x, 9x and 11x.

We know that sum of all the interior angles of the hexagon is equal to 720° and obviously, the largest angle is 11x. We just have to calculate the value of x.

x + 3x + 5x + 7x + 9x + 11x = 720°

36x = 720°

x = 20°

11x = 11(20°) = 220°

Therefore, the largest interior angle of the hexagon is 220°.

Additional answers:-

x = 20°

3x = 60°

5x = 100°

7x = 140°

9x = 180°