Question

prove that the sum of angles of a hexagon is 720°​

Answer 1

Answer:

Hexagon has 6 sides

The sum of all interior angles of a polygon with n sides is

=> (n-2)180.

Here , the hexagon has 6 sides.So n =6.

=> (6-2)×180

=> 4×180

=> 720.

Answer 2

Required Answer :-

As per the question we can say that :

• ABCDEF is a hexagon

we have to prove :

• ∠A + ∠B+ ∠C+ ∠D+ ∠E+ ∠F= 720°

Construction To be done :

• Join AC, AD and AE.

Proof:

➙ In ΔABC , ∠1+ ∠B + ∠5= 180° (Sum of the three angles of a triangle is 180° ) ...(i)

➙ In Δ ACD, ∠2+∠6+∠7= 180° (Sum of the three angles of a triangle is 180° ) ...(ii)

➙ In Δ ADE, ∠3+∠8+ ∠9 = 180° (Sum of the three angles of a triangle is 180° ) (iii)

➙ In Δ AEF, ∠4 + ∠10 + ∠F = 180° (Sum of the three angles of a triangle is 180° ) (iv)

Adding (i) , (ii) , (iii) and (iv), we get,

➙ (∠1+ ∠B+ ∠5) + (∠2+ ∠6+ ∠7) + ( ∠3 + ∠8+ ∠9) + ( ∠4 + ∠10+ ∠F) = 720°

➙ (∠1+ ∠2+ ∠3+ ∠4) + ∠B + ( ∠5+ ∠6) + (∠7+ ∠8) + ∠9+ ∠10) + ∠F = 720°

$\begin{gathered} \longrightarrow \quad\underline{\boxed { \textbf{\textsf{∠A + ∠B+ ∠C+ ∠D+ ∠E+ ∠F= 720}}^\circ }} \\ \end{gathered}$