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TRINA DAS

· started a discussion

· 1 Months ago

Clarify (Question:357372.0)

How does ∠1 + ∠2 + ∠3 + ∠4 + ∠5= 180º come?

Question:

In the given figure, what is the value of ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 + ∠8 + ∠9 + ∠10 = ? 

  

Options:
A)

600

B)

720

C)

900

D)

1080

Solution:

  

We have,

∠2 + ∠4 + ∠7 = 180º

∠3 + ∠5 + ∠6 = 180º

∠1 + ∠3 + ∠8 = 180º

∠2 + ∠5 + ∠9 = 180º

∠1 + ∠4 + ∠10 = 180º

Adding all,

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 + ∠8 + ∠9 + ∠10

= 900º – (∠1 + ∠2 + ∠3 + ∠4 + ∠5)

∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 180º  (Given in the solution figure)

= 900º – 180º = 720º

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