Question

The interior angles of a hexagon are in the ratio 3:3:4:4:5:5. Find all the angles of the hexagon.​

Answer 1

$\huge\bigstar\mathbb\red{solution} \bigstar$

The interior angles of a hexagon are in the ratio 3:3:4:4:5:5 .

Let angles are

$3x,3x,4x,4x,5x,5x$

Sum of all angles of a polygon , having a sides

$= 180°(n - 2) \\ \\ = 180°(6 - 2) \\ \\ = 180° \times 4 \\ \\ =720°$

Now ,

$3x + 3x + 4x + 4x + 5x + 5x = 720° \\ \\ 24x = 720° \\ \\ x = \frac{720°}{24} \\ \\ x = 30°.$

$3x = 3 \times 30° = 90 °\\ 3x =3 \times 30° = 90° \\ 4x = 4 \times 30° = 120° \\ 4x = 4 \times 30° = 120° \\ 5x = 5 \times 30° = 150°\\ 5x = 5 \times 30 °= 150°.$