Answer: (a) [tex]77\dfrac17^{\circ}[/tex] (b) 180°
Explanation:
Sum of interior angles of a polygon with n-sides: [tex](n-2)\times180^{\circ}[/tex]
In hexagon, total sides: n =6
Given: The interior angles of a hexagon are in the ratio 3:3:4:5:6:7.
Let the angles be 3x , 3x, 4x, 5x, 6x, 7x
Then,
[tex]3x+3x+4x+5x+6x+7x=(6-2)\times180^{\circ}\\\\\Rightarrow\ 28x=4\times 180\\\\\\\Rightarrow\ x=\dfrac{4\times180}{28}\\\\\Rightarrow\ x=25\dfrac{5}{7}^{\circ}[/tex]
Smallest angle= 3x = [tex]3\times \dfrac{180}{7}=77\dfrac17^{\circ}[/tex]
Largest angle = 7x =[tex]7\times\dfrac{180}{7}=180^{\circ}[/tex]
