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love history [14]
3 years ago
12

The interior angles of a hexegon are in the ratio 3:3:4:5:6:7. Find; (a) The size of the smallest angle. (b) The size of the lar

gest angle​
Business
1 answer:
stiks02 [169]3 years ago
4 0

Answer: (a) 77\dfrac17^{\circ}  (b) 180°

Explanation:

Sum of interior angles of a polygon with n-sides: (n-2)\times180^{\circ}

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,

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}

Smallest angle= 3x = 3\times \dfrac{180}{7}=77\dfrac17^{\circ}

Largest angle = 7x =7\times\dfrac{180}{7}=180^{\circ}

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