Question

One angle of a hexagon is 140° and the remaining angles are in the ratio 4 : 3 : 4 : 5 : 4. Calculate the measures of the smallest and the largest angles.

Answer 1

A hexagon has 6 sides
∴ Sum of interior angles
= (n - 2) x 180°
= (6- 2) x 180°
= 4 x 180° = 720°
One angle is given to be 140°
Ratio of the remaining five angles
= 4 : 3 : 4 : 5: 4
∴ The interior angles are 4x°, 3x°, 4x°, 5x° and 4x°
∴ 140° + 4x° + 3x° + 4x° + 5° + 4x° = 720°
⇒ 20x° + 140° = 720°
⇒ x° = `(580°)/(20)` = 29°
The smallest angle is 3x° = 3.29° = 87°
The largest angle is 5x° = 5.29° = 145°.